外文翻译

五分钟搞定5000字－外文文献翻译工具大全 /node/2151在科研过程中阅读翻译外文文献是一个非常重要的环节，许多领域高水平的文献都是外文文献，借鉴一些外文文献翻译的经验是非常必要的。

由于特殊原因我翻译外文文献的机会比较多，慢慢地就发现了外文文献翻译过程中的三大利器：Google“翻译”频道、金山词霸（完整版本）和CNKI“翻译助手"。

具体操作过程如下：1.先打开金山词霸自动取词功能，然后阅读文献；2.遇到无法理解的长句时，可以交给Google处理，处理后的结果猛一看，不堪入目，可是经过大脑的再处理后句子的意思基本就明了了；3.如果通过Google仍然无法理解，感觉就是不同，那肯定是对其中某个“常用单词”理解有误，因为某些单词看似很简单，但是在文献中有特殊的意思，这时就可以通过CNKI的“翻译助手”来查询相关单词的意思，由于CNKI的单词意思都是来源与大量的文献，所以它的吻合率很高。

另外，在翻译过程中最好以“段落”或者“长句”作为翻译的基本单位，这样才不会造成“只见树木，不见森林”的误导。

注：1、Google翻译：/language_toolsgoogle，众所周知，谷歌里面的英文文献和资料还算是比较详实的。

我利用它是这样的。

一方面可以用它查询英文论文，当然这方面的帖子很多，大家可以搜索，在此不赘述。

回到我自己说的翻译上来。

下面给大家举个例子来说明如何用吧比如说“电磁感应透明效应”这个词汇你不知道他怎么翻译，首先你可以在CNKI里查中文的，根据它们的关键词中英文对照来做，一般比较准确。

在此主要是说在google里怎么知道这个翻译意思。

大家应该都有词典吧，按中国人的办法，把一个一个词分着查出来，敲到google里，你的这种翻译一般不太准，当然你需要验证是否准确了，这下看着吧，把你的那支离破碎的翻译在google里搜索，你能看到许多相关的文献或资料，大家都不是笨蛋，看看，也就能找到最精确的翻译了，纯西式的！我就是这么用的。

引言概述：在现代高等教育中，毕业设计（或称为毕业论文、学士论文等）是学生完成学业的重要环节。

而对于一些特定的专业，例如翻译专业，有时候还需要完成外文翻译这一项任务。

本文将探讨毕设外文翻译的意义和目的，以及为什么对翻译专业的学生而言这一任务极其重要。

正文内容：1.提高翻译能力和技巧外文翻译是一项对翻译专业学生而言十分重要的任务，通过进行外文翻译，学生们可以通过实践提高自己的翻译能力和技巧。

在这个过程中，他们可以学习如何处理不同类型的外文文本，熟悉不同领域的专业术语，并掌握一些常用的翻译技巧和策略。

2.扩展语言和文化知识毕设外文翻译要求学生们对翻译语言的相关知识和背景有一定的了解。

在进行翻译时，学生们需要遵循目标语言的语法规则，并确保所翻译的内容准确、清晰地传达源语言的意义。

通过这一过程，学生们可以进一步扩展自己的语言和文化知识，提高自己的跨文化沟通能力。

3.提供实践机会毕设外文翻译为学生们提供了一个实践的机会，让他们能够将在课堂上所学到的理论知识应用于实际操作中。

通过实践，学生们可以对所学知识的理解更加深入，同时也可以发现并解决实际翻译过程中的问题和挑战。

这对于学生们将来从事翻译工作时具备更好的实践能力和经验具有重要意义。

4.培养翻译专业素养毕设外文翻译要求学生们具备良好的翻译专业素养。

在进行翻译过程中，学生们需要保持专业的态度和责任心，严谨地对待每一个翻译任务。

他们需要学会如何进行翻译质量的评估和控制，以确保最终翻译稿的准确性和流畅性。

这一系列的要求和实践，可以帮助学生们培养出色的翻译专业素养。

5.提升自我学习和研究能力毕设外文翻译要求学生们进行广泛的文献阅读和研究，以便更好地理解所翻译的内容，并找到适当的翻译方法和策略。

在这个过程中，学生们需要培养自己的自主学习和研究能力，提高对学术和专业领域的敏感性，并能够独立思考和解决问题。

这将对学生们未来的学术研究和进一步的职业发展产生积极的影响。

总结：引言概述:毕业设计外文翻译（Thesis Translation）是指在毕业设计过程中，对相关外文文献进行翻译，并将其应用于研究中，以提供理论支持和参考。

本科毕业论文外文翻译外文译文题目:不确定条件下生产线平衡：鲁棒优化模型和最优解解法学院：机械自动化专业：工业工程学号: 201003166045学生姓名: 宋倩指导教师：潘莉日期: 二○一四年五月Assembly line balancing under uncertainty: Robust optimization modelsand exact solution methodÖncü Hazır , Alexandre DolguiComputers ＆Industrial Engineering，2013,65：261–267不确定条件下生产线平衡：鲁棒优化模型和最优解解法安库·汉泽，亚历山大·多桂计算机与工业工程，2013，65：261–267摘要这项研究涉及在不确定条件下的生产线平衡，并提出两个鲁棒优化模型。

假设了不确定性区间运行的时间。

该方法提出了生成线设计方法,使其免受混乱的破坏。

基于分解的算法开发出来并与增强策略结合起来解决大规模优化实例.该算法的效率已被测试,实验结果也已经发表。

本文的理论贡献在于文中提出的模型和基于分解的精确算法的开发.另外，基于我们的算法设计出的基于不确定性整合的生产线的产出率会更高，因此也更具有实际意义。

此外,这是一个在装配线平衡问题上的开创性工作,并应该作为一个决策支持系统的基础。

关键字：装配线平衡；不确定性; 鲁棒优化；组合优化；精确算法1.简介装配线就是包括一系列在车间中进行连续操作的生产系统。

零部件依次向下移动直到完工。

它们通常被使用在高效地生产大量地标准件的工业行业之中。

在这方面，建模和解决生产线平衡问题也鉴于工业对于效率的追求变得日益重要。

生产线平衡处理的是分配作业到工作站来优化一些预定义的目标函数。

那些定义操作顺序的优先关系都是要被考虑的,同时也要对能力或基于成本的目标函数进行优化。

就生产（绍尔，1999）产品型号的数量来说，装配线可分为三类：单一模型（SALBP）,混合模型(MALBP）和多模式（MMALBP）。

外文文献原稿和译文原稿DATABASEA database may be defined as a collection interrelated data store together with as little redundancy as possible to serve one or more applications in an optimal fashion .the data are stored so that they are independent of programs which use the data .A common and controlled approach is used in adding new data and in modifying and retrieving existing data within the data base .One system is said to contain a collection of database if they are entirely separate in structure .A database may be designed for batch processing , real-time processing ,or in-line processing .A data base system involves application program, DBMS, and database.THE INTRODUCTION TO DATABASE MANAGEMENT SYSTEMSThe term database is often to describe a collection of related files that is organized into an integrated structure that provides different people varied access to the same data. In many cases this resource is located in different files in different departments throughout the organization, often known only to the individuals who work with their specific portion of the total information. In these cases, the potential value of the information goes unrealized because a person in other departments who may need it does not know it or it cannot be accessed efficiently. In an attempt to organize their information resources and provide for timely and efficient access, many companies have implemented databases.A database is a collection of related data. By data, we mean known facts that can be recorded and that have implicit meaning. For example, the names, telephone numbers, and addresses of all the people you know. You may have recorded this data in an indexed address book, or you may have stored it on a diskette using a personalcomputer and software such as DBASE Ⅲor Lotus 1-2-3. This is a collection of related data with an implicit meaning and hence is a database.The above definition of database is quite general. For example, we may consider the collection of words that made up this page of text to be usually more restricted. A database has the following implicit properties:● A database is a logically coherent collection of data with some inherent meaning. A random assortment of data cannot be referred to as a database.● A database is designed, built, and populated with data for a specific purpose. It has an intended group of user and some preconceived applications in which these users are interested.● A database represents some aspect of the real world, sometimes called the miniworld. Changes to the miniworld are reflected in the database.In other words, a database has some source from which data are derived, some degree of interaction with events in the real world, and an audience that is actively interested in the contents of the database.A database management system (DBMS) is composed of three major parts: (1) a storage subsystem that stores and retrieves data in files; (2)a modeling and manipulation subsystem that provides the means with which to organize the data and to add, delete, maintain, and update the data; and (3) an interface between the DBMS and its users. Several major trends are emerging that enhance the value and usefulness of database management systems.●Managers who require more up-to-date information to make effective decisions.●Customers who demand increasingly sophisticated information services and more current information about the status of their orders, invoices, and accounts.●Users who find that they can develop custom applications with database systems in a fraction of the time it takes to use traditional programming languages.●Organizations that discover information has a strategic value; they utilize their database systems to gain an edge over their competitors.A DBMS can organize, process, and present selected data elements from the database. This capability enables decision makers to search, probe, and query database contents in order to extract answers to nonrecurring and unplanned questions that aren’t available in regular reports. These questions might initially be vague and/or p oorly defined, but people can “browse” through the database until they have the needed information. In short, the DBMS will “mange” the stored data items and assemble the needed items from the common database in response to the queries of those who aren’t programmers. In a file-oriented system, user needing special information may communicate their needs to a programmer, who, when time permits, will write one or more programs to extract the data and prepare the information. The availability of a DBMS, however, offers users a much faster alternative communications path.DATABASE QUERYIf the DBMS provides a way to interactively enter and update the database ,as well as interrogate it ,this capability allows for managing personal database. However, it does not automatically leave an audit trail of actions and does not provide the kinds of controls necessary in a multi-user organization .There controls are only available when a set of application programs is customized for each data entry and updating function.Software for personal computers that perform some of the DBMS functions has been very popular .Individuals for personal information storage and processing intended personal computers for us .Small enterprises, professionals like doctors, architects, engineers, lawyers and so on have also used these machines extensively. By the nature of intended usage ,database system on there machines are except from several of the requirements of full-fledged database systems. Since data sharing is not intended, concurrent operations even less so ,the software can be less complex .Security and integrity maintenance are de-emphasized or absent .as data volumes will be small, performance efficiency is also less important .In fact, the only aspect of a database system that is important is data independence. Data independence ,as stated earlier ,means that application programs and user queries need not recognize physical organization of data on secondary storage. The importance of this aspect , particularly for the personal computer user ,is that this greatly simplifies database usage . The user can store ,access and manipulate data at ahigh level (close to the application)and be totally shielded from the low level (close to the machine )details of data organization.DBMS STRUCTURING TECHNIQUESSpatial data management has been an active area of research in the database field for two decades ,with much of the research being focused on developing data structures for storing and indexing spatial data .however, no commercial database system provides facilities for directly de fining and storing spatial data ,and formulating queries based on research conditions on spatial data.There are two components to data management: history data management and version management .Both have been the subjects of research for over a decade. The troublesome aspect of temporal data management is that the boundary between applications and database systems has not been clearly drawn. Specifically, it is not clear how much of the typical semantics and facilities of temporal data management can and should be directly incorporated in a database system, and how much should be left to applications and users. In this section, we will provide a list of short-term research issues that should be examined to shed light on this fundamental question.The focus of research into history data management has been on defining the semantics of time and time interval, and issues related to understanding the semantics of queries and updates against history data stored in an attribute of a record. Typically, in the context of relational databases ,a temporal attribute is defined to hold a sequence of history data for the attribute. A history data consists of a data item and a time interval for which the data item is valid. A query may then be issued to retrieve history data for a specified time interval for the temporal attribute. The mechanism for supporting temporal attributes is to that for supporting set-valued attributes in a database system, such as UniSQL.In the absence of a support for temporal attributes, application developers who need to model and history data have simply simulated temporal attributes by creating attribute for the time interval ,along with the “temporal” attribute. This of course may result in duplication of records in a table, and more complicated search predicates in queries. The one necessary topic of research in history data management is to quantitatively establish the performance (and even productivity) differences betweenusing a database system that directly supports attributes and using a conventional database system that does not support either the set-valued attributes or temporal attributes.Data security, integrity, and independenceData security prevents unauthorized users from viewing or updating the database. Using passwords, users are allowed access to the entire database of the database, called subschemas. For example, an employee database can contain all the data about an individual employee, but one group of users may be authorized to view only payroll data, while others are allowed access to only work history and medical data.Data integrity refers to the accuracy, correctness, or validity of the data in the database. In a database system, data integrity means safeguarding the data against invalid alteration or destruction. In large on-line database system, data integrity becomes a more severe problem and two additional complications arise. The first has to do with many users accessing the database concurrently. For example, if thousands of travel agents book the same seat on the same flight, the first agent’s booking will be lost. In such cases the technique of locking the record or field provides the means for preventing one user from accessing a record while another user is updating the same record.The second complication relates to hardware, software or human error during the course of processing and involves database transaction which is a group of database modifications treated as a single unit. For example, an agent booking an airline reservation involves several database updates (i.e., adding the passenger’s name and address and updating the seats-available field), which comprise a single transaction. The database transaction is not considered to be completed until all updates have been completed; otherwise, none of the updates will be allowed to take place.An important point about database systems is that the database should exist independently of any of the specific applications. Traditional data processing applications are data dependent.When a DMBS is used, the detailed knowledge of the physical organization of the data does not have to be built into every application program. The application program asks the DBMS for data by field name, for example, a coded representationof “give me customer name and balance due” would be sent to the DBMS. Without a DBMS the programmer must reserve space for the full structure of the record in the program. Any change in data structure requires changes in all the applications programs.Data Base Management System (DBMS)The system software package that handles the difficult tasks associated with creating ,accessing and maintaining data base records is called a data base management system (DBMS). A DBMS will usually be handing multiple data calls concurrently.It must organize its system buffers so that different data operations can be in process together .It provides a data definition language to specify the conceptual schema and most likely ,some of the details regarding the implementation of the conceptual schema by the physical schema.The data definition language is a high-level language, enabling one to describe the conceptual schema in terms of a “data model “.At the present time ,there are four underling structures for database management systems. They are :List structures.Relational structures.Hierarchical (tree) structures.Network structures.Management Information System(MIS)An MIS can be defined as a network of computer-based data processing procedures developed in an organization and integrated as necessary with manual and other procedures for the purpose of providing timely and effective information to support decision making and other necessary management functions.One of the most difficult tasks of the MIS designer is to develop the information flow needed to support decision making .Generally speaking ,much of the information needed by managers who occupy different levels and who have different levels and have different responsibilities is obtained from a collection of exiting information system (or subsystems)Structure Query Language (SQL)SQL is a data base processing language endorsed by the American NationalStandards Institute. It is rapidly becoming the standard query language for accessing data on relational databases .With its simple ,powerful syntax ,SQL represents a great progress in database access for all levels of management and computing professionals.SQL falls into two forms : interactive SQL and embedded SQL. Embedded SQL usage is near to traditional programming in third generation languages .It is the interactive use of SQL that makes it most applicable for the rapid answering of ad hoc queries .With an interactive SQL query you just type in a few lines of SQL and you get the database response immediately on the screen.译文数据库数据库可以被定义为一个相互联系的数据库存储的集合。

Strengths优势All these private sector banks hold strong position on CRM part, they have professional, dedicated and well-trained employees.所以这些私人银行在客户管理部分都持支持态度，他们拥有专业的、细致的、训练有素的员工。

Private sector banks offer a wide range of banking and financial products and financial services to corporate and retail customers through a variety of delivery channels such as ATMs, Internet-banking, mobile-banking, etc. 私有银行通过许多传递通道（如自动取款机、网上银行、手机银行等）提供大范围的银行和金融产品、金融服务进行合作并向客户零售。

The area could be Investment management banking, life and non-life insurance, venture capital and asset management, retail loans such as home loans, personal loans, educational loans, car loans, consumer durable loans, credit cards, etc. 涉及的领域包括投资管理银行、生命和非生命保险、风险投资与资产管理、零售贷款（如家庭贷款、个人贷款、教育贷款、汽车贷款、耐用消费品贷款、信用卡等）。

Private sector banks focus on customization of products that are designed to meet the specific needs of customers. 私人银行主要致力于为一些特殊需求的客户进行设计和产品定制。

本科毕业论文外文翻译Undergraduate Thesis External Translation (700 Words)Title: The Impact of Social Media on Consumer Behavior Abstract:With the rapid development of social media, its influence on consumer behavior has drawn increasing attention from scholars and marketers. This paper aims to explore the impact of social media on consumer behavior from the perspective of information acquisition, interpersonal communication, and brand evaluation. Through a literature review and analysis, it is found that social media has a significant impact on consumer behavior by providing easy access to information, facilitating communication between consumers, and influencing brand perception. This research provides valuable insights for marketers in understanding and utilizing social media platforms to effectively engage with consumers and influence their purchasing decisions.1. IntroductionSocial media has become an integral part of people's daily lives, and its impact on consumer behavior cannot be ignored. This paper aims to investigate the impact of social media on consumer behavior and provide practical implications for marketers. The research question is: How does social media influence consumer behavior in terms of information acquisition, interpersonal communication, and brand evaluation?2. Information Acquisition2.1 Social media provides a platform for consumers to easilyaccess information about products and services. Through social media platforms such as Facebook, Instagram, and Twitter, consumers can obtain product reviews, comparisons, and recommendations from peers. This information influences consumers' purchasing decisions and enhances their knowledge about products.2.2 Social media also serves as a source of entertainment and inspiration, enabling users to discover new trends and products. Influencers and celebrities, who gain popularity through social media, often endorse products and create consumer desire for these items. This form of indirect advertising through social media has a significant impact on consumer behavior.3. Interpersonal CommunicationSocial media platforms enable users to interact with friends, family, and even strangers. This communication aspect of social media hasa direct influence on consumer behavior.3.1 Word-of-mouth (WOM) communication through social media is prevalent. Consumers often share their positive or negative experiences with products on social media platforms, which influence others' opinions and purchasing decisions. These online conversations have a wide reach and can greatly impact brand perception.3.2 Social media facilitates communication between consumers and brands. Consumers can directly communicate with brands through social media channels, providing feedback, asking questions, and seeking assistance. This two-way communicationimproves customer satisfaction and loyalty.4. Brand Evaluation4.1 Social media plays a crucial role in brand evaluation. Consumers often seek information about brands, their values, and their reputation on social media platforms. Positive or negative brand mentions and reviews on social media greatly influence consumers' perceptions of brands, leading to either increased or decreased brand trust and loyalty.4.2 Social media influencers and celebrities endorsing particular brands also impact brand evaluation. These individuals' recommendations and opinions can greatly influence consumers' perceptions and preferences for specific brands.5. ConclusionIn conclusion, social media has a significant impact on consumer behavior by influencing information acquisition, interpersonal communication, and brand evaluation. Marketers should utilize and engage with social media platforms to effectively reach and influence their target customers. This research provides insights for marketers to enhance their social media strategies and create effective brand-consumer interactions.。

外文文献资料1、Software EngineeringSoftware is the sequences of instructions in one or more programming languages that comprise a computer application to automate some business function. Engineering is the use of tools and techniques in problem solving. Putting the two words together, software engineering is the systemtic application of tools and techniques in the development of computer-based applications.The software engineering process describes the steps it takes to deelop the system. We begin a development project with the notion that there is a problem to be solved via automation. The process is how you get from problem recognition to a working solution. A quality process is desirable because it is more likely to lead to a quality product. The process followed by a project team during the development life cycle of an application should be orderly, goal-oriented, enjoyable, and a learning experience.Object-oriented methodology is an approach to system lifecycle development that takes a top-down view of data objects, their allowable actions, and the underlying communication requirement to define a system architecture. The data and action components are encapsulated, that is , they are combined together, to form abstract data types Encapsulation means that if I know what data I want ,I also know the allowable processes against that data. Data are designed as lattice hierarchies of relationships to ensure that top-down, hierarchic inheritance and side ways relationships are accommodated. Encapsulated objects are constrained only to communicate via messages. At a minimum, messages indicate the receiver and action requested. Messages may be more elaborate, including the sender and data to be acted upon.That we try to apply engineering discipline to software development does not mean that we have all the answers about how to build applications. On the contrary, we still build systems that are not useful and thus are not used. Part of the reason for continuing problems in application development, is that we are constantly trying to hita moving target. Both the technology and the type of applications needed by businesses are constantly changing and becoming more complex. Our ability to develop and disseminate knowledge about how to successfully build systems for new technologies and new application types seriously lags behind technological and business changes.Another reason for continuing problems in application development is that we aren’t always free to do what we like and it is hard to change habits and cultures from the old way of doing things, as well as get users to agree with a new sequence of events or an unfamiliar format for documentation.You might ask then, if many organizations don’t use good software engineering practices, why should I bother learning them? There are two good answers to this question. First, if you never know the right thing to do, you have no chance of ever using it. Second, organizations will frequently accept evolutionary, small steps of change instead of revolutionary, massive change. You can learn individual techniques that can be applied without complete devotion to one way of developing systems. In this way, software engineering can speed changee in their organizations by demonstrating how the tools and techniques enhance th quality of both the product and the process of building a system.2、Data Base System1、IntroductionThe development of corporate databases will be one of the most important data-processing activities for the rest of the 1970s. Date will be increasingly regarded as a vital corporate resource, which must be organized so as to maximize their value. In addition to the databases within an organization, a vast new demand is growing for database services, which will collect, organize, and sell data.The files of data which computers can use are growing at a staggering rate. The growth rate in the size of computer storage is greater than the growth in the size or power of any other component in the exploding data processing industry. The more data the computers have access to, the greater is their potential power. In all walks of life and in all areas of industry, data banks will change the areas of what it is possiblefor man to do. In the end of this century, historians will look back to the coming of computer data banks and their associated facilities as a step which changed the nature of the evolution of society, perhaps eventually having a greater effect on the human condition than even the invention of the printing press.Some most impressive corporate growth stories of the generation are largely attributable to the explosive growth in the need of information.The vast majority of this information is not yet computerized. However, the cost of data storage hardware is dropping more rapidly than other costs in data processing. It will become cheaper to store data on computer files than to store them on paper. Not only printed information will be stored. The computer industry is improving its capability to store line drawing, data in facsimile form, photo-graphs, human speech, etc. In fact, any form of information other than the most intimate communications between humans can be transmitted and stored digitally.There are two main technology developments likely to become available in the near future. First, there are electromagnetic devices that will hold much more data than disks but have much longer access time. Second, there are solid-state technologies that will give microsecond access time but capacities are smaller than disks.Disks themselves may be increased in capacity somewhat. For the longer term future there are a number of new technologies which are currently working in research labs which may replace disks and may provide very large microsecond-access-time devices. A steady stream of new storage devices is thus likely to reach the marketplace over the next 5 years, rapidly lowering the cost of storing data.Given the available technologies, it is likely that on-line data bases will use two or three levels of storage. One solid-state with microsecond access time, one electromagnetic with access time of a fraction of a second. If two ,three ,or four levels of storage are used, physical storage organization will become more complex ,probably with paging mechanisms to move data between the levels; solid-state storage offers the possibility of parallel search operation and associativememory.Both the quantity of data stored and the complexity of their organization are going up by leaps and bounds. The first trillion bit on-line stores are now in use . in a few year’s time ,stores of this size may be common.A particularly important consideration in data base design is to store the data so that the can be used for a wide variety of applications and so that the way they can be changed quickly and easily. On computer installation prior to the data base era it has been remarkably difficult to change the way data are used. Different programmers view the data in different ways and constantly want to modify them as new needs arise modification , however ,can set off a chain reaction of changes to existing programs and hence can be exceedingly expensive to accomplish .Consequently , data processing has tended to become frozen into its old data structures .To achieve flexibility of data usage that is essential in most commercial situations . Two aspects of data base design are important. First, it should be possible to interrogate and search the data base without the lengthy operation of writing programs in conventional programming languages. Second ,the data should be independent of the programs which use them so that they can be added to or restructured without the programs being changed .The work of designing a data base is becoming increasing difficult , especially if it is to perform in an optimal fashion . There are many different ways in which data can be structured ,and they have different types of data need to be organized in different ways. Different data have different characteristics , which ought to effect the data organization ,and different users have fundamentally different requirements. So we need a kind of data base management system(DBMS)to manage data.Data base design using the entity-relationship model begins with a list of the entity types involved and the relationships among them. The philosophy of assuming that the designer knows what the entity types are at the outset is significantly different from the philosophy behind the normalization-based approach.The entity-relationship(E-R)approach uses entity-relationship diagrams. The E-Rapproach requires several steps to produre a structure that is acceptable by the particular DBMS. These steps are:(1) Data analysis(2) Producing and optimizing the entity model.(3) Logical schema development(4) Physical data base design process.Developing a data base structure from user requirements is called data bases design. Most practitioners agree that there are two separate phases to the data base design process. The design of a logical database structure that is processable by the data base management system(DBMS)d escribes the user’s view of data, and is the selection of a physical structure such as the indexed sequential or direct access method of the intended DBMS.Current data base design technology shows many residual effects of its outgrowth from single-record file design methods. File design is primarily application program dependent since the data has been defined and structured in terms of individual applications to use them. The advent of DBMS revised the emphasis in data and program design approaches.There are many interlocking questions in the design of data-base systems and many types of technique that one can use is answer to the question so many; in fact, that one often sees valuable approaches being overlooked in the design and vital questions not being asked.There will soon be new storage devices, new software techniques, and new types of data bases. The details will change, but most of the principles will remain. Therefore, the reader should concentrate on the principles.2、Data base systemThe conception used for describing files and data bases has varied substantially in the same organization.A data base may be defined as a collection of interrelated data stored together with as little redundancy as possible to serve on or more applications in an optimal fashion; the data are stored so that they are independent of programs which use thedata; a common and controlled approach is used in adding new data and in modifying and retrieving existing data within the data base. One system is said to contain a collection of data bases if they are entirely separate in structure.A data base may be designed for batch processing, real-time processing, or in-line processing. A data base system involve application program, DBMS, and data base.One of the most important characteristics of most data bases is that they will constantly need to change and grow. Easy restructuring of the data base must be possible as new data types and new applications are added. The restructuring should be possible without having to rewrite the application program and in general should cause as little upheaval as possible. The ease with which a data base can be changed will have a major effect on the rate at which data-processing application can be developed in a corporation.The term data independence is often quoted as being one of the main attributes of a data base. It implies that the data and the application programs which use them are independent so that either may be changed without changing the other. When a single set of data items serves a variety of applications, different application programs perceive different relationships between the data items. To a large extent, data-base organization is concerned with the representation of relationship between data items and records as well as how and where the data are stored. A data base used for many applications can have multiple interconnections between the data item about which we may wish to record. It can describes the real world. The data item represents an attribute, and the attribute must be associated with the relevant entity. We design values to the attributes, one attribute has a special significance in that it identifies the entity.An attribute or set of attribute which the computer uses to identify a record or tuple is referred to as a key. The primary key is defined as that key used to uniquely identify one record or tuple. The primary key is of great importance because it is used by the computer in locating the record or tuple by means of an index or addressing algorithm.If the function of a data base were merely to store data, its organization would be simple. Most of the complexities arise from the fact that is must also show the relationships between the various items of data that are stored. It is different to describe the data in logical or physical.The logical data base description is referred to as a schema .A schema is a chart of the types of data that one used. It gives the names of the entities and attributes, and specifics the relations between them. It is a framework into which the values of the data-items can be fitted.We must distinguish between a record type and a instance of the record. When we talk about a “personnel record”,this is really a record type.There are no data values associated with it.The term schema is used to mean an overall chart of all of the dataitem types and record types stored in a data he uses. Many different subschema can be derived from one schema.The schema and the subschema are both used by the data-base management system, the primary function of which is to serve the application programs by executing their data operations.A DBMS will usually be handing multiple data calls concurrently. It must organize its system buffers so that different data operations can be in process together. It provides a data definition language to specify the conceptual schema and most likely, some of the details regarding the implementation of the conceptual schema by the physical schema. The data definition language is a high-level language, enabling one to describe the conceptual schema in terms of a “data model” .The choice of a data model is a difficult one, since it must be rich enough in structure to describe significant aspects of the real world, yet it must be possible to determine fairly automatically an efficient implementation of the conceptual schema by a physical schema. It should be emphasized that while a DBMS might be used to build small data bases, many data bases involve millions of bytes, and an inefficient implementation can be disastrous.We will discuss the data model in the following.3、Three Data ModelsLogical schemas are defined as data models with the underlying structure of particular database management systems superimposed on them. At the present time, there are three main underlying structures for database management systems. These are :RelationalHierarchicalNetworkThe hierarchical and network structures have been used for DBMS since the 1960s. The relational structure was introduced in the early 1970s.In the relational model, the entities and their relationships are represented by two-dimensional tables. Every table represents an entity and is made up of rows and columns. Relationships between entities are represented by common columns containing identical values from a domain or range of possible values.The last user is presented with a simple data model. His and her request are formulated in terms of the information content and do not reflect any complexities due to system-oriented aspects. A relational data model is what the user sees, but it is not necessarily what will be implemented physically.The relational data model removes the details of storage structure and access strategy from the user interface. The model provides a relatively higher degree of data. To be able to make use of this property of the relational data model however, the design of the relations must be complete and accurate.Although some DBMS based on the relational data model are commercially available today, it is difficult to provide a complete set of operational capabilities with required efficiency on a large scale. It appears today that technological improvements in providing faster and more reliable hardware may answer the question positively.The hierarchical data model is based on a tree-like structure made up of nodes and branches. A node is a collection of data attributes describing the entity at that point.The highest node of the hierarchical tree structure is called a root. The nodes at succeeding lower levels are called children .A hierarchical data model always starts with a root node. Every node consists of one or more attributes describing the entity at that node. Dependent nodes can follow the succeeding levels. The node in the preceding level becomes the parent node of the new dependent nodes. A parent node can have one child node as a dependent or many children nodes. The major advantage of the hierarchical data model is the existence of proven database management systems that use the hierarchical data model as the basic structure. There is a reduction of data dependency but any child node is accessible only through its parent node, the many-to –many relationship can be implemented only in a clumsy way. This often results in a redundancy in stored data.The network data model interconnects the entities of an enterprise into a network. In the network data model a data base consists of a number of areas. An area contains records. In turn, a record may consist of fields. A set which is a grouping of records, may reside in an area or span a number of areas. A set type is based on the owner record type and the member record type. The many-to many relation-ship, which occurs quite frequently in real life can be implemented easily. The network data model is very complex, the application programmer must be familiar with the logical structure of the data base.4、Logical Design and Physical DesignLogical design of databases is mainly concerned with superimposing the constructs of the data base management system on the logical data model. There are three mainly models: hierarchical, relational, network we have mentioned above.The physical model is a framework of the database to be stored on physical devices. The model must be constructed with every regard given to the performance of the resulting database. One should carry out an analysis of the physical model with average frequencies of occurrences of the grou pings of the data elements, with expected space estimates, and with respect to time estimates for retrieving and maintaining the data.The database designer may find it necessary to have multiple entry points into a database, or to access a particular segment type with more than one key. To provide this type of access; it may be necessary to invert the segment on the keys. Thephysical designer must have expertise in knowledge of the DBMS functions and understanding of the characteristics of direct access devices and knowledge of the applications.Many data bases have links between one record and another, called pointers. A pointer is a field in one record which indicates where a second record is located on the storage devices.Records that exist on storage devices is a given physical sequence. This sequencing may be employed for some purpose. The most common pupose is that records are needed in a given sequence by certain data-processing operations and so they are stored in that sequences.Different applications may need records in different sequences.The most common method of ordering records is to have them in sequence by a key —that key which is most commonly used for addressing them. An index is required to find any record without a lengthy search of the file.If the data records are laid out sequentially by key, the index for that key can be much smaller than they are nonsequential.Hashing has been used for addressing random-access storages since they first came into existence in the mid-1950s. But nobody had the temerity to use the word hashing until 1968.Many systems analysis has avoided the use of hashing in the suspicion that it is complicated. In fact, it is simple to use and has two important advantages over indexing. First, it finds most records with only one seek and second, insertion and deletions can be handled without added complexity. Indexing, however, can be used with a file which is sequential by prime key and this is an overriding advantage, for some batch-pro-cessing applications.Many data-base systems use chains to interconnect records also. A chain refers to a group of records scatters within the files and interconnected by a sequence of pointers. The software that is used to retrive the chained records will make them appear to the application programmer as a contiguous logical file.The primary disadvantage of chained records is that many read operations areneeded in order to follow lengthy chains. Sometimes this does not matter because the records have to be read anyway. In most search operations, however, the chains have to be followed through records which would not otherwise to read. In some file organizations the chains can be contained within blocked physical records so that excessive reads do not occur.Rings have been used in many file organizations. They are used to eliminate redundancy. When a ring or a chain is entered at a point some distance from its head, it may be desirable to obtain the information at the head quickly without stepping through all the intervening links.5、Data Description LanguagesIt is necessary for both the programmers and the data administrator to be able to describe their data precisely; they do so by means of data description languages. A data description language is the means of declaring to data-base management system what data structures will be used.A data description languages giving a logical data description should perform the folloeing functions:It should give a unique name to each data-item type, file type, data base and other data subdivision.It should identify the types of data subdivision such as data item segment , record and base file.It may define the type of encoding the program uses in the data items (binary , character ,bit string , etc.)It may define the length of the data items and the range of the values that a data item can assume .It may specify the sequence of records in a file or the sequence of groups of record in the data base .It may specify means of checking for errors in the data .It may specify privacy locks for preventing unauthorized reading or modification of the data .These may operate at the data-item ,segment ,record, file or data-base level and if necessary may be extended to the contents(value) of individual data items .The authorization may , on the other hand, be separate defined .It is more subject to change than the data structures, and changes in authorization proceduresshould not force changes in application programs.A logical data description should not specify addressing ,indexing ,or searching techniques or specify the placement of data on the storage units ,because these topics are in the domain of physical ,not logical organization .It may give an indication of how the data will be used or of searching requirement .So that the physical technique can be selected optimally but such indications should not be logically limiting.Most DBMS have their own languages for defining the schemas that are used . In most cases these data description languages are different to other programmer language, because other programmer do not have the capability to define to variety of relationship that may exit in the schemas.附录 B 外文译文1、软件工程软件是指令的序列，该指令序列由一种或者多种程序语言编写，它能使计算机应用于某些事物的运用自动化。

In traditional supply chain inventory management, orders are the only information firms exchange, but information technology now allows firms to share demand and inventory data quickly and inexpensively. We study the value of sharing these data in a model with one supplier, N identical retailers, and stationary stochastic consumer demand. There are inventory holding costs and back-order penalty costs. We compare a traditional information policy that does not use shared information with a full information policy that does exploit shared information. In a numerical study we find that supply chain costs are 2.2% lower on averagewith the full information policy than with the traditional information policy, and themaximum difference is 12.1%. We also develop a simulation-based lower bound over all feasible policies. The cost difference between the traditional information policy and the lower bound is an upper bound on the value of information sharing: In the same study, that difference is 3.4% on average, and no more than 13.8%. We contrast the value of information sharing with two other benefits of information technology, faster and cheaper order processing, which lead to shorter lead times and smaller batch sizes, respectively. In our sample, cutting lead times nearly in half reduces costs by 21% on average, and cutting batchesin half reduces costs by 22% on average. For the settings we study, we conclude that implementing information technology to accelerate and smooth the physical flow of goods through a supply chain is significantly more valuable than using information technology to expand the flow of information.Inventory management is a commercial enterprise management of the core areas, Enterprises can also achieve an effective key, if we can achieve from the purchase of stock,Sales then the entire flow of goods and capital flow situation for the unified management and reasonable production, timely sales and inventory is the smallest. reduce the backlog of material, then the business will achieve the best results.1.sessionIn my experience, session word is probably second only to the extent of the abuse of transaction, even more interesting is the transaction and the session in the context of the meaning of some of the same.session, the Chinese often translated into the session, its original meaning refers to the beginnings and ends of a series of action / information, such as a phone call from the dial to pick up the phone to hang up the middle of the process can be described as a series of session. Sometimes we can see that the case "during the session in a browser session ,...", term used here is its original meaning, is open from a browser window to close the period of ①. The most confusing is the "user (client) during the first session," the words, it may refer to a series of user actions (generally with a specific purpose related to a series of actions, such as log on to buy goods from to sign out such an online shopping checkout process, sometimes also called a transaction), but sometimes may be just that a connection could also be that the meaning of ①, the difference can only be inferred by context ②.However, when the term session is associated with the network protocol when it often implies a "connection-oriented" and / or "on hold" so the two meanings, "connection-oriented" refers to both the communication in the communication prior to first establish a communication channel, such as phone calls, until the other party answered the phone communication can begin, and this is the opposite of writing, before you sent the letter, the time you and can not confirm the other side of the address is correct, communication channels Buyi Ding can be established,but the sender, the communication has already begun. "Keep state" means the communication party is able to associate a series of messages, making messages between each other depends, for example, a waiter can recognize old customers come back and remember the last time the customer still owes a store, dollar . Examples of this type, "a TCP session" or "a POP3 session"③.And to the web server flourishing, session in the context of semantic web development has a new expansion, its meaning is mean to the client and server to maintain state between the solution ④. Session is also sometimes used to refer to such solutions, storage structures, such "stored in the session to xxx where" ⑤. For various 用于web development languages are available to some extent on the support of such a solution, so in the context of a particular language 下, session also used to denote a solution on behalf of the language, such as regular Java in the provision of javax.servlet.http.HttpSession referred to as the session ⑥.In view of this confusion has been changed, in this article use the term session will have different meanings depending on the context, drew attention to the resolution.In this article, the use of Chinese "during the browser session," to convey the meaning of ①, use "session mechanism" to convey the meaning ④, use the "session" expression meaning ⑤, use specific "HttpSession" to convey the meaning ⑥Second, HTTP protocol and the state to maintainHTTP protocol itself is stateless, HTTP protocol which is consistent with the original purpose of the client only needs a simple request to download some file server, either the client or the server not have been necessary records of past behavior to each other, and each time between the request are independent, like a customer and a vending machine or an ordinary (non-membership) as the relationship between supermarkets.However, smart (or greedy?) People soon discovered that if they can provide on-demand generation of dynamic web information will become more useful, like a cable TV with on-demand the same function. This demand on the one hand to force gradually add HTML form, script, DOM and other client-side behavior, on the other hand there is the server-side CGI practices to respond to client-side dynamic request, the HTTP protocol as the transport carrier also added a file upload , cookie these characteristics. The role which cookie is to solve the stateless HTTP protocol efforts defects. As for the subsequent emergence of the session mechanism is yet another in between the client and the server state solution.Let us use some examples to describe the session cookie and the differences and similarities between the mechanisms. I once frequented a coffee shop with free gifts to drink five cups of coffee offers a cup of coffee, but a one-time consumption of five cups of coffee is remote, then need a way to record a customer's consumption. Imagine that in fact nothing less than the following several options:1, the store's staff is very powerful, able to remember each customer's consumption, as long as customers entered the cafe, shop assistants know how to deal with the. This approach is the agreement itself to support the state.2, issue customers a card recording the number of consumers in general have a validity period. Each consumer, if this card is produced, then the consumer will be with the consumer before or after linking up. This approach is maintained in the client state.3, a membership card issued to customers, in addition to any information outside the card number is not recorded, each consumer, if the card is produced, then the records clerk in the store to find the card number corresponds to the record to add some consumer information. Thisapproach is maintained in the server-side state.As the HTTP protocol is stateless, but due to various considerations do not want to become a state, therefore, the last two programs has become a realistic option. Specifically cookie mechanism is used to maintain state of the client program, which uses a session mechanism to maintain state in the server-side program. We also see that, thanks to server-side maintain state of the program in customer client but also Xuyaobaocun a logo, so mechanisms may need the help of session cookie mechanism to identify the purpose of Da Dao saved, it actually alternatives are available.Third, the cookie mechanismThe basic principle cookie mechanism as simple as the above example, but there are several issues to resolve: "membership card" how to distribute; "membership card" of the content; and customers how to use the "Member Card."Orthodox cookie distribution is by extending the HTTP protocol to achieve, and the server through the HTTP response header with a line of special instructions to prompt the browser in accordance with the instructions generates the corresponding cookie. But pure client-side scripting such as JavaScript or VBScript can also generate the cookie.The cookie used by the browser in the background according to certain principles automatically sent to the server. Check all stored browser cookie, if a cookie is greater than or equal scope statement will be the location of the requested resources, put the resources of the HTTP request cookie attached to the head sent the request to the server. Means that McDonald's membership card can only be produced in the McDonald's store, if a store has also issued its own membership card, then enter the store when the addition to produce McDonald's membership card, but also to produce a member of the store card.cookie's contents include: name, values, expiration time, path and domain.You can specify a domain in which a domain such as. , the equivalent of main store signs, such as Procter & Gamble, you can also specify a specific domain of a machine under such or , can float Flexibility to do than.Path is the name behind the URL with the path, such as / or / foo, etc., can do more than a counter Rejoice.Path together with the domain constitutes a cookie's scope. If you do not set the expiration time, then the lifetime of this cookie to the browser during the session, simply close the browser window, cookie disappears. This period of life of the cookie browser session is called session cookie. Session cookie is generally not stored on the hard disk but kept in memory, of course, provided that it is not standardized. If you set the expiration time, the browser the cookie will be saved to the hard disk, open again after closing the browser, the cookie is still valid until the expiration time exceeds a set.Stored in a cookie on your hard disk in a different browser, shared between processes, such as the two IE windows. And stored in memory for the cookie, different browsers have different approaches. For IE, open windows in a press Ctrl-N (or from the File menu) to open the window can be shared with the original window while using other means to open the IE process will not have to open the windows shared memory cookie; for Mozilla Firefox0.8, all of the process and can share the same tab the cookie. In general is the window.open javascript window will open with the original windows shared memory cookie. Browser, this cookie for the session cookiedoes not believe that people only recognize the approach to the use of the regular session of web application development mechanism causing great distress.Here is a goolge set cookie response header exampleHTTP/1.1 302 FoundLocation: /intl/zh-CN/Set-Cookie: PREF = ID = 0565f77e132de138: NW = 1: TM = 1098082649: LM = 1098082649: S = KaeaCFPo49RiA_d8; expires = Sun, 17-Jan-2038 19:14:07 GMT; path = /; domain =. google . comContent-Type: text / htmlThis is the use of HTTPLook the HTTP Sniffer HTTP communications software to capture the part of the recordGoolge browser to access the resources again, automatically send out cookieUse Firefox can easily observe the current value of cookieUse HTTPLook with Firefox cookie can easily understand the working principle.IE can be set to ask before accepting cookieThis is a dialog box asking to accept cookie.Fourth, understand the session mechanismmechanism is a server-side session mechanism, the server uses a hash table is similar to the structure (and probably is to use a hash table) to save the information.When the program needs for a client's request to create a session when the server first checks the client's request is included in a session ID - known as the session id, if the description contains a session id for this client previously Create over session, the server in accordance with the session id to retrieve the session out of the use (if not retrieved, may be the new one), if the client request does not include session id, then create a session for this client and generate a session with this associated with the session id, session id value should be a not only will not repeat, not easy to find the law to copy the string, the session id to be returned in this response to the client saved.Save the session id of the ways to use cookie, so the interaction of the browser can automatically identify this play by the rules to the server. The name of this cookie are generally similar to SEEESIONID, and. For example, web applications weblogic generated cookie, JSESSIONID = ByOK3vjFD75aPnrF7C2HmdnV6QZcEbzWoWiBYEnLerjQ99zWpBng! -145788764, Its name is JSESSIONID.As the cookie can be artificially prohibited, there must be other mechanisms to be banned in the cookie when the session id still be able to pass back to the server. Often use a technique called URL rewriting, the session id is attached to the URL path directly behind, there are two additional ways, one is the URL path as additional information, showing the form of http:// ... .. / xxx; jsessionid = ByOK3vjFD75aPnrF7C2HmdnV6QZcEbzWoWiBYEnLerjQ99zWpBng! -145788764 The other is as a URL query string appended to the back, showing the form of http://.. (xxx)jsessionid=ByOK3vjFD75aPnrF7C2HmdnV6QZcEbzWoWiBYEnLerjQ99zWpBng!-145788764Both ways is no different for users, and only a server parsing the time to deal with the different ways, using the first ways are conducive to turning one kind of session id's information and to distinguish normal program parameters.Wei Liao Zai the interaction always maintain state, we must each client may request a path to the rear of containing this session id.Another technique known as hidden form fields. Is that the server will automatically modify the form, add a hidden field, so when the form is submitted to the session id passed back to the server. Example, the following form<form name="testform" action="/xxx"><input type="text"></ Form>Being passed to client will be rewritten before<form name="testform" action="/xxx"><input type="hidden" name="jsessionid"value="ByOK3vjFD75aPnrF7C2HmdnV6QZcEbzWoWiBYEnLerjQ99zWpBng!-145788764"><input type="text"></ Form>Application of this technology is now less, I contacted the very old iPlanet6 (SunONE Application Server's predecessor) on the use of this technology.In fact this technology can simply apply to the action URL rewriting instead.When talking about the session mechanism, often heard of such a misunderstanding, "as long as the browser is closed, session disappears." In fact, imagine the example card, unless the customer to make sales on the store card, otherwise the store would not easily remove the customer information. This is also true of the session, unless the procedure to inform the server to delete a session, otherwise the server will remain on the program are generally done in the user log off when the send a command to delete the session. However, the browser will never take the initiative to notify the server will be shut off, so the server will not have the opportunity to know the browser has been the reason why there is such a misconception, the majority of session mechanism to use a session cookie to store the session id and close your browser the session id is gone, once again connect to the server will not be able to find when the original session. If the server cookie settings are saved to the hard disk, or use some means to rewrite the browser's HTTP request header sent to the original session id sent to the server, then re-open the browser can still find the original session.It is precisely because of the closure does not cause the browser session is deleted, forcing server seesion set up a failure time, as the distance between the first use of the client session for more than the failure time, the server that the client has ceased its activities, the session will be deleted to save storage space.5, javax.servlet.http.HttpSessionHttpSession session mechanism is the Java platform implementation of norms, because it isonly the interface, specific to each web application server providers, in addition to standard support, there will still be no requirement of some norms in the nuances. Here we are with BEA's Weblogic Server8.1 as an example to demonstrate.First of all, Weblogic Server provides a set of parameters to control its HttpSession implementation, including the use of cookie switch option to use URL rewriting switches, session persistence settings, session failure time setting, as well as for the cookie a variety of settings, such as set cookie name, path, domain, cookie survival time.In general, session are stored in memory, when the process is stopped, or restart the server when the memory of the session will also be empty, if you set the session persistence feature, the server will save the session to your hard drive When the server process restart or the information can be used again, Weblogic Server supports sustainable manner including documents, databases, client-side cookie preservation and reproduction.Strictly speaking not a persistent copy saved, because the session is actually stored in memory, but the same information is replicated to each server process within the cluster, so even if a server process to stop working and still available from other processes obtain session.cookie settings will affect the survival time of the browser generates a session cookie is a cookie. The default is to use a session cookie. Interested can use it to test us in the fourth quarter, as mentioned in the misunderstanding.cookie path for the web application is a very important option, Weblogic Server on the default handling of this option makes it significantly different from other servers. We will discuss the topic later.Settings on the session reference [5] /wls/docs70/webapp/weblogic_xml.html # 10368696, HttpSession Frequently Asked Questions (In this section the implications for the session mixed ⑤and ⑥)1, session is created whenA common misconception is that the session in a client visit, was created, but the fact is that until a server-side program called HttpServletRequest.getSession (true) when such a statement is created, note that if the JSP does not appear to use <% @ page session = "false"%> closed session, the JSP file will be automatically compiled into a Servlet when the inclusion of such a statement HttpSession session = HttpServletRequest.getSession (true); This is also implied in JSP session object origin.As the session will consume memory resources, so if you do not intend to use the session, all the JSP should be turned off it.2, session is deleted whenComprehensive discussions earlier, session is deleted in the following cases a. program calls HttpSession.invalidate (); or b. from the last time before the client sends the session id than the interval session timeout settings; or c. server process is stopped (non-persistent session)3, how to do delete the browser closed session。

Stability of hybrid system limit cycles: application to the compass gait biped RobotIan A. Hiskens'Department of Electrical and Computer EngineeringUniversity of Illinois at Urbana-ChampaignUrbana IL 61801 USAAbstractLimit cycles are common in hybrid systems. However the non-smooth dynamics of such systems makes stability analysis difficult. This paper uses recent extensions of trajectory sensitivity analysis to obtain the characteristic multipliers of non-smooth limit cycles. The stability of a limit cycle is determined by its characteristic multipliers. The concepts are illustrated using a compass gait biped robot example.1 IntroductionHybrid system are characterized by interactions between continuous (smooth) dynamics and discrete events. Such systems are common across a diverse range of application areas. Examples include power systems [l], robotics [2, 3], manufacturing [4] and air-traffic control [5]. In fact, any system where saturation limits are routinely encountered can be thought of as a hybrid system. The limits introduce discrete events which (often) have a significant influence on overall behaviour.Many hybrid systems exhibit periodic behaviour. Discrete events, such as saturation limits, can act to trap the evolving system state within a constrained region of state space. Therefore even when the underlying continuous dynamics are unstable, discrete events may induce a stable limit set. Limit cycles (periodic behaviour) are often created in this way. Other systems, such as robot motion, are naturally periodic.Limit cycles can be stable (attracting), unstable (repelling) or non-stable (saddle). The stability of periodic behaviour is determined by characteristic (or Floquet) multipliers. A periodic solution corresponds to a fixed point of a Poincare map. Stability of the periodic solution is equivalent to stability of the fixed point. The characteristic multipliers are the eigenvalues of the Poincare map linearized about the fixed point. Section 4 reviews the connection between this linearized map and trajectory sensitivities.Poincare maps have been used to analyse the stability of limit cycles in various forms of hybrid systems. However calculation of the underlying trajectory sensitivities has relied upon particular system structures, see for example [7, 8], or numerical differencing, for example [6]. This paper uses a recent generalization of trajectory sensitivity analysis [9] to efficiently detemine the stability of limit cycles in hybrid systems.A hybrid system model is given in Section 2. Section 3 develops the associated variational equations. This is followed in Section 4 by a review of stability analysis of limit cycles. Conclusions and extensions are presented in Section 5.2 ModelDeterministic hybrid systems can be represented by a model that is adapted from a differential-algebraic (DAE) structure. Events are incorporated via impulsive action and switching of algebraic equations, giving the Impulsive Switched (DAIS) modelwheren x R ∈ are dynamic states and my R ∈ are algebraic states;(.)δ is the Dirac delta;(.)u is the unit-step function;,:n mnj f h RR +→；(0)(),:i n mng gR R ±+→; some elements of each(.)gwill usually be identicallyzero, but no elements of the composite g should be identically zero; the()i g± aredefined with the same form as g in (2), resulting in a recursive structure for g;,dey yare selected elements of y that trigger algebraic switching and state reset(impulsive) events respectively;dyandeymay share common elements.The impulse and unit-step terms of the DAIS model can be expressed in alternative forms:Each impulse term of the summation in (1) can be expressed in the state reset formwhere the notation x+denotes the value of x just after the reset event, whilstx-andy-refer to the values of x and y just prior to the event.The contribution of each()i g± in (2) can be expressed aswith (2) becomingThis form is often more intuitive than (2).It can be convenient to establish the partitionswherex -are the continuous dynamic states, for example generator angles, velocities andfluxes;z are discrete dynamic states, such as transformer tap positions and protection relay logic states;λ are parameters such as generator reactances, controller gains and switching times. The partitioning of the differential equations f ensures that away from events,x -evolves according to .(,)x y f x --=, whilst z and λ remain constant. Similarly,the partitioning of the reset equationsjhensures thatx -and λ remain constantat reset events, but the dynamic states z are reset to new values given by(,)jh y x z--+=-. The model can capture complex behaviour, from hysteresis and non-windup limits through to rule-based systems [l]. A more extensive presentation of this model is given in [9].Away from events, system dynamics evolve smoothly according to the familiardifferential-algebraic modelwhere g is composed of(0)gtogether with appropriate choices of()i g- or()i g+ ,depending on the signs of the corresponding elements of yd. At switching events (2),some component equations of g change. To satisfy the new g = 0 equation, algebraic variables y may undergo a step change. Reset events (3) force a discrete change in elements of x. Algebraic variables may also step at a reset event to ensure g= 0 is satisfied with the altered values of x. The flows of and y are defined respectively aswhere x(t) and y(t) satisfy (l),(2), along with initial conditions,3 'Ikajectory SensitivitiesSensitivity of the flowsxφandyφto initial conditionsxare obtained bylinearizing (8),(9) about the nominal trajectory,The time-varying partial derivative matrices given in (12),(13) are known as trajectory sensitiuities, and can be expressed in the alternative formsThe formxx ,xy provides clearer insights into the development of thevariational equations describing the evolution of the sensitivities. The alternative form 0(,)x t x φ, 0(,)yt x φ highlights the connection between the sensitivities and the associated flows. It is shown in Section 4 that these sensitivities underlie the linearization of the Poincare map, and so play a major role in determining the stability of periodic solutions.Away from events, where system dynamics evolve smoothly, trajectory sensitivities 0xx andxy are obtained by differentiating (6),(7) withrespect to 0x.This giveswhere/xf x f≡∂∂, and likewise for the other Jacobian matrices. Note that,,,xyxyf fg gare evaluated along the trajectory, and hence are time varyingmatrices. It is shown in 19, 101 that the numerical solution of this(potentially high order) DAE system can be obtained as a by-product of numerically integrating the original DAE system (6),(7). The extra computational cost is minimal. Initial conditions forxx are obtained from (10) aswhere I is the identity matrix. Initial conditions for 0zy follow directly from(17),Equations (16),(17) describe the evolution of the sensitivitiesxx andxybetween events. However at an event, the sensitivities are generally discontinuous. It is necessary to calculate jump conditions describing the step change inxx andxy . For clarity, consider a single switching/reset event, so the model (1),(2) reduces(effectively) to the formLet （(),()x y ττ） be the point where the trajectory encounters the triggering hypersurface s(x,y) = 0, i.e., the point where an event is initiated. This point is called the junction point and r is the junction time. It is assumed the encounter is transversal.Just prior to event triggering, at time τ-, we haveSimilarly,,y x++are defined for time τ+, just after the event has occurred. It isshown in [9] that the jump conditions for the sensitivitiesxx are given byThe assumption that the trajectory and triggering hypersurface meet transversally ensures a non-zero denominator for 0x τ The sensitivitiesxy . immediatelyafter the event are given byFollowing the event, i.e., for t τ+>, calculation of the sensitivities proceeds according to (16),(17) until the next event is encountered. The jump conditions provide the initial conditions for the post-event calculations.4 Limit Cycle AnalysisStability of limit cycles can be determined using Poincare maps [11, 12]. This section provides a brief review of these concepts, and establishes the connection with trajectory sensitivities.A Poincark map effectively samples the flow of a periodic system once every period. The concept is illustrated in Figure 1. If the limit cycle is stable, oscillations approach the limit cycle over time. The samples provided by the corresponding Poincare map approach a fixed point. A non-stable limit cycle results in divergent oscillations. For such a case the samples of the Poincare map diverge.To define a Poincare map, consider the limit cycle Γshown in Figure 1. Let ∑ be a hyperplane transversal to Γ at*x. The trajectory emanating from*xwill again encounter ∑ at*xafter T seconds, where T is the minimum period of the limit cycle. Due to the continuity of the flowxφwith respect to initial conditions, trajectories starting on ∑ in a neighbourhood of*x. will, in approximately T seconds, intersect ∑ in the vicinity of*x. Hencexφand ∑define a mappingwhere()kT x ττ≈ is the time taken for the trajectory to return to ∑. Complete details can hefound in [11,12]. Stability of the Paincare map (22) is determined by linearizing P at the fixed point*x, i.e.,From the definition of P(z) given by (22), it follows that DP(*x) is closely related to thetrajectory sensitivities***(,)(,)xxT T x x xφφ∂≡∂. In fact, it is shown in [11] thatwhereσ is a vector normal to ∑.The matrix*(,)xT x φis exactly the trajectory sensitivity matrix after one period of the limitcycle, i.e., starting from*xand returning to*x. This matrix is called the Monodromymatrix .It is shown in [11] that for an autonomous system, one eigenvalue of *(,)xT x φ isalways 1, and the corresponding eigenvector lies along **(,)f y x The remaining eigenvalues*(,)xT x φof coincide with the eigenvalues of DP(*x ), and are known as the characteristicmultipliers mi of the periodic solution. The characteristic multipliers are independent of the choice of cross-section ∑ . Therefore, for hybrid systems, it is often convenient to choose ∑ as a triggering hypersurface corresponding to a switching or reset event that occurs along the periodic solution.Because the characteristic multipliers mi are the eigenvalues of the linear map DP(x*), they determine the stability of the Poincarb map P(kx), and hence the stability of the periodic solution.Three cases are of importance: 1. Alli m lie within the unit circle, i.e., 1im<,i ∀.The map is stable, so the periodicsolution is stable. 2. Allim lie outside the unit circle. The periodic solution is unstable.3. Someim lie outside the unit circle. The periodic solution is non-stable.Interestingly, there exists a particular cross-section*∑, such thatwhere *ς∈∑.This cross-section*∑is the hyperplane spanned by the n - 1 eigenvectors of*(,)xT x φthat are not aligned with **(,)f y x . Therefore the vector *σthat is normal to*∑ is the left eigenvector of *(,)xT x φ corresponding to the eigenvalue 1. The hyperplane*∑is invariant under*(,)xT x φ, i.e., **(,)f y x maps vectors *ς∈∑back into*∑.5 ConclusionsHybrid systems frequently exhibit periodic behaviour. However the non-smooth nature of such systems complicates stability analysis. Those complications have been addressed in this paper throughapplication of a generalization of trajectory sensitivity analysis. Deterministic hybrid systems can be represented by a set ofdifferential-algebraic equations, modified to incorporate impulse (state reset) action and constraint switching. The associated variational equations establish jump conditions that describe the evolution of sensitivities through events. These equations provide insights into expansion/contraction effects at events. This is a focus of future research.Standard Poincar6 map results extend naturally to hybrid systems. The Monodromy matrix is obtained by evaluating trajectory sensitivities over one period of the (possibly non-smooth) cyclical behaviour. One eigenvalue of this matrix is always unity. The remaining eigenvalues are the characteristic multipliers of the periodic solution. Stability is ensured if all multipliers lieReferences[l] LA. Hiskens and M.A. Pai, “Hybrid systems view of power system modelling,” in Proceedings of the IEEE International Symposium on Circuits and Systems, Geneva, Switzerland, May 2000.[2] M.H. Raibert, Legged Robots That Balance, MIT Press, Cambridge, MA, 1986.[3] A. Goswami, B. Thuilot, and B. Espiau, “A study of the passive gait of a compass-like biped ro bot: symmetry and chaos,’’ International Journal of Robotics Research, vol. 17, no. 15, 1998.[4] S. Pettersson, “Analysis and design of hybrid systems,” Ph.D. Thesis, Department of Signals and Systems, Chalmers University of Technology, Goteborg, Sweden, 1999.[5] C. Tomlin, G. Pappas, and S. Sastry, “Conflict resolution for air traffic management:A study in multiagent hybrid systems,” IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 509-521, April 1998.[6] A. Goswami, B. Espiau, and A. Keramane, “Limit cycles in a passive compass gait biped and passivity-mimicking contr ol laws,” Journal of Au tonomous Robots, vol. 4, no. 3, 1997. 171 B.K.H. Wong, H.S.H. Chung, and S.T.S. Lee, ‘Computation of the cycle state-variable sensitivity matrix of PWM DC/DC converters and its applica tion,” IEEE Transactions on Circuit s and Systems I, vol. 47, no. 10, pp. 1542-1548, October 2000.[8] M. Rubensson, B. Lennartsson, and S. Petters son, “Convergence to limit cycles in hybrid systems - an example,” in Prepri nts of 8th International Federation of Automatic Control Symposium on Large Scale Systems: Theo y d Applications, Rio Patras, Greece, 1998, pp. 704-709.[9] I.A. Hiskens and M.A. Pai, “Trajectory sensitivity analysis of hyhrid systems,” IEEE Transactions on Circuits and Systems I, vol. 47, no. 2, pp. 204-220, February 2000.[10]D. Chaniotis, M.A. Pai, and LA. Hiskens, “Sen sitivity analysis of differential-algebraic systems using the GMRES method - Ap plication to power systems,” in Proceedings of the IEEE International Symposium on Circuits and Systems, Sydney, Australia, May 2001.[11]T.S Parker and L.O. Chua, Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, New York, NY, 1989.[12]R. Seydel, Practical Bifurcation and Stability Analysis, Springer-Verlag. New York, 2nd edition, 1994.。

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