Stability of Switched Dynamical Systems

切换动力系统的稳定性

• 批准号: 0400306
• 负责人: Kumpati Narendra
• 金额: --
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-04-15 至 2008-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0400306&HistoricalAwards=false
• 关键词: Stability; Switched; Dynamical; Systems

The objective of control is to in .uence the behavior of dynamical systems.Achiev-ing fast and accurate control under di .erent environmental conditions,even whileassuring stability and robustness,is the aim of all control system design.Whenenvironmental changes are signi .cant (e.g.faults o subsystem failures)the designmay equire the use of multiple controllers,each of which is appropriate in a speci .ccontext.By a switching system we mean a hybrid dynamical system with a decisionmechanism which orchestrates the switching between di .erent controllers.With greatadvances in computer technology,and the concomitant increase in the complexity ofdynamical systems,switching system are becoming ubiquitous.The analysis andsynthesis of such systems is consequently assuming major importance.Stability is the primary equirement of any control system.Once this is assured,optimization of the performance of the overall system can be undertaken within aframework of stability.Following this,modi .cations in the control laws can be un-dertaken to make the system robust under di .erent perturbations.This is the basicphilosophy used in conventional control system design as well as in this proposal.Even though research on switching systems has been in progress for many years andnumerous contributions have been made to the .eld,basic questions still remain unan-swered.For example the stability of many classes of linear,nonlinear,and adaptiveswitching systems still remains to be answered,and very little progress has been madein shaping the transient response resulting from the switching action.Both of theseimportant issues are included in the proposal.The proposal consists of three parts.Since stability is undoubtedly the most impor-tant unresolved issue,the .rst part of the proposal is devoted to it.Switching betweengeneral linear time-invariant systems and positive linear systems is treated in this con-text.Special attention is given to systems with diagonal Lyapunov functions in viewof their importance to switching in decentralized systems.Also treated are piecewiselinear systems which are practically important and theoretically tractable.Followingthis,in the second part of the proposal,the performance that can be achieved byswitching is considered.The third and last part of the proposal is devoted to switch-ing in adaptive systems.Intellectual Merit: The PI believes that the research proposed addresses funda-mental questions whose solutions are essential for a better understanding of switchingsystems.This in turn is vital for the design of future control systems.Broader Impacts: The esearch proposed will enhance collaboration between thePI and other international esearchers (particularly Dr.Robert Shorten at the Hamil-ton Institute,Ireland and Dr.Jens Kalkuhl of Daimler-Chrysler Research),lead toincreased interaction with industry,and most important of all,provide training toboth graduate and undergraduate students on advanced control techniques.1

控制的目的是控制动态系统的行为。在不同的环境条件下实现快速而准确的控制，即使在保证稳定性和鲁棒性的同时，也是所有控制系统设计的目标。当环境变化显著(例如，子系统故障)时，设计可以等同于使用多个控制器，每个控制器在特定的上下文中是适当的。我们所说的切换系统是指具有协调不同控制器之间切换的决策机制的混合动态系统。随着计算机技术的巨大进步，以及随之而来的动态系统的复杂性的增加，切换系统变得越来越普遍。这类系统的分析和综合因此变得非常重要。稳定性是任何控制系统的首要要求。一旦稳定性得到保证，就可以在稳定的框架内对整个系统的性能进行优化。在此基础上，可以对控制律进行修改，以使系统在不同的扰动下具有鲁棒性。这是常规控制系统设计中使用的基本思想，也是在本方案中使用的基本思想。尽管对切换系统的研究已经进行了多年，并对该领域做出了许多贡献，但在控制系统的设计中，对切换系统的分析和综合是非常重要的。尽管对切换系统的研究已经在稳定的框架内进行了多年，并且对控制律进行了修改，以使系统在不同的扰动下具有鲁棒性。这是常规控制系统设计中使用的基本思想，也是在本方案中使用的基本思想。尽管对切换系统的研究已经进行了多年，并且对该领域做出了许多贡献，但是，对于切换系统的性能的优化可以在稳定的框架内进行基本问题仍未解决。例如，许多线性、非线性和自适应切换系统的稳定性仍有待回答，而在形成由开关动作引起的暂态响应方面进展甚微。这两个重要问题都包括在建议中。建议由三部分组成。由于稳定性无疑是最重要的未解决问题，本文讨论了一般线性时不变系统与正线性系统之间的切换问题。鉴于对角线Lyapunov函数对分散系统切换的重要性，本文重点讨论了对角线Lyapunov函数对分散系统切换的重要性。此外，还讨论了具有实际重要性和理论上易处理的分段线性系统。接着，在方案的第二部分，建议的第三部分和最后部分致力于自适应系统中的切换。智力优点：PI认为所提出的研究解决了基本问题，其解决方案对于更好地理解切换系统是必不可少的。这反过来对于未来控制系统的设计是至关重要的。广泛的影响：所提出的研究将加强PI和其他国际研究人员(特别是爱尔兰哈米尔顿研究所的Robert Shorten博士和戴姆勒-克莱斯勒研究公司的Jens Kalkuhl博士)之间的合作，导致与业界增加互动，最重要的是，为研究生和本科生提供先进控制技术方面的培训1