Worst-case optimal regulation of linear systems in the presence of structured perturbations (Q2735067)

The worst-case optimal regulation of linear time-varying systems in the presence of both parameter perturbations and exogenous input is considered. Two cases for parameter perturbations are considered: Case I for an \(L_\infty\) perturbation of the parameters and Case II for an \(L_2\) perturbation of the parameters. The ratio of disturbance energy to the controlled system energy is taken as the performance criterion for an \(H_\infty\) control problem. Necessary conditions which are satisfied by an optimal control and the worst-case exogenous disturbances for the worst variation of system parameters are developed, by Pontryagin's minimum principle. Necessary conditions are given in terms of nonlinear two-point-boundary-valued problems. Thus, the optimal control is an open-loop one in contrast to the \(H_\infty\) control problem where the synthesis of the output feedback controller is required.NEWLINENEWLINEFor the entire collection see [Zbl 0962.00004].