Issues in Robust Controller Design and the Theory of Dynamic Games

鲁棒控制器设计和动态博弈理论中的问题

• 批准号: 9113153
• 负责人: Tamer Basar
• 金额: $ 8万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-15 至 1994-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9113153&HistoricalAwards=false
• 关键词: Issues; Robust; Controller; Design; Theory

This proposal describes a research plan to develop a time-domain based theory for the characterization of minimax controllers for linear and nonlinear finite-dimensional systems with norm-bounded and partially stochastic uncertainties, and for the analysis of their robustness with regard to modeling inaccuracies and order reduction. A further topic of study will be the characterization of robust controllers for a (parametrized) family of plants and under multiple criteria. The general approach to be adopted in this study is that of dynamic or differential game theory, which provides the most natural setting for these worst-case design problems, in both discrete and continuous time, and under different types of measurement schemes. For each class of problems, a relationship will be established between the worst-case controller performance and the upper value of a particular zero-sum dynamic game, which will facilitate a further robustness analysis in terms of admissibility, and sensitivity to unmodeled fast plant dynamics and weak subsystem coupling. The game-theoretic approach will also allow for multiple performance criteria and partial stochastic modeling. Research efforts along the lines described in the proposal should lead to major advances in the methodology and design of worst-case controllers for various types of systems, as well as to some new fundamental results in the theory of dynamic games.

该提案描述了一项研究计划，旨在为具有范数有界和部分随机不确定性的线性和非线性有限维系统的极大极小控制器的表征开发基于时域的理论。并对其在建模误差和降阶方面的鲁棒性进行了分析。进一步的研究主题将是（参数化）植物家族和多标准下的鲁棒控制器的表征。本研究将采用的一般方法是动态或微分博弈论，它为这些最坏情况设计问题提供了最自然的设置，无论是在离散时间还是连续时间，以及在不同类型的测量方案下。对于每一类问题，将建立最坏情况控制器性能与特定零和动态博弈的上值之间的关系，这将有助于在可容许性方面进行进一步的鲁棒性分析，以及对未建模的快速植物动力学和弱子系统耦合的敏感性。博弈论方法也将允许多个性能标准和部分随机建模。沿着提案中描述的路线进行的研究工作将导致各种类型系统的最坏情况控制器的方法和设计方面的重大进展，以及动态博弈理论中的一些新的基本结果。