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.
