Feedback stabilization along a path of steady-states for 1-D semilinear heat and wave equations

Jean-Michel Coron (1) , Emmanuel Trélat (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We report the problem of feedback stabilization along a path of steady-states, and of exact boundary controllability of semilinear one-dimensional heat and wave equations. The main result is that it is possible to move from any steady-state to any other one by means of a boundary control, provided that they are in the same connected component of the set of steady-states. The proof is based on an effective feedback stabilization procedure which is efficiently implementable.

Domaines: Optimisation et contrôle [math.OC]

Jean-Michel Coron, Emmanuel Trélat. Feedback stabilization along a path of steady-states for 1-D semilinear heat and wave equations. 2005, 6 p. ⟨hal-00086458⟩