On Optimized Feedback Control and the Robustification of Opimal Controls

We consider a system that is exactly controllable. For given initial state, terminal state and objective function, an optimal control is often well-defined. Such an optimal control has the disadvantage that although it works perfectly well for the given initial state, for a perturbed initial state it often does not make sense. In this talk we present a concept to obtain robust control schemes by the combination of the optimal control with a stabilizing feedback law. In this way, also for perturbed initial states the system is controlled in a reasonable way. In the talk we focus on the boundary control of the wave equation. However, our concept is applicable to the control of general time-dependent systems.