Issues in Robust Controller Design and the Theory of Dynamic Games

该提案描述了一项研究计划， 基于时域理论的表征 线性和非线性极大极小控制器 有限维系统的范数有界和 部分随机不确定性，并为分析 在建模方面的鲁棒性 不准确和订单减少。 另一个主题是 研究将是鲁棒控制器的表征 对于（参数化）植物家族， 多重标准 拟采取的一般做法 本文主要研究动态或微分对策 理论，它提供了最自然的设置， 这些最坏情况的设计问题，在离散和 连续时间，在不同类型的 测量方案。 对于每一类问题， 将在最坏情况之间建立关系 控制器性能和a的上限值 特别是零和动态博弈，这将有助于 在可接受性方面的进一步鲁棒性分析， 和对未建模的快速工厂动态的敏感性， 弱子系统耦合 博弈论 该方法还将允许多种性能 标准和部分随机建模。 研究 沿着提案中描述的路线所做的努力应 在方法和设计方面取得重大进展 最坏情况控制器的各种类型的系统，如 以及该理论中的一些新的基本结果 动态游戏。

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.