Worst-Case Optimal Control of Linear Systems in the Presence of Parameter Perturbations

Worst-case optimal regulation of linear time varying systems in the presence of both parameter perturbations as well as exogenous inputs is considered. The control problem is presented as a state space minimax problem. Necessary conditions for the optimal solutions are derived for the worst disturbances, the worst parameter perturbations, and the optimal controller. The necessary conditions are given in terms of a nonlinear two-point-boundary-value problem. The results are illustrated by examples.