Martin Gugat — Page 2

arXiv2013

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.

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arXiv2010

Boundary feedback stabilization by piecewise constant time delay for the wave equation

For vibrating systems, a delay in the application of a feedback control can destroy the stabilizing effect of the control. In this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with delay at the other end. We show that for certain feedback parameters the system is exponentially stable with constant delays of the form 4L/c, 8L/c, 12L/c ... Moreover, we show that the system is exponentially stable with piecewise constant delays that attain the values 4L/c and 8L/c.

math.OC↗