On Optimized Feedback Control and the Robustification of Opimal Controls

TL;DR

This paper introduces a method to enhance the robustness of optimal controls by integrating them with stabilizing feedback laws, ensuring effective control even under initial state perturbations, demonstrated on boundary control of wave equations.

Contribution

It proposes a novel approach combining optimal control with feedback stabilization to improve robustness against initial state perturbations.

Findings

Robust control schemes are effective for perturbed initial states.

The method is applicable to boundary control of wave equations.

Potential for generalization to other time-dependent systems.

Abstract

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.