An approximation method for exact controls of vibrating systems

Nicolae Cindea (1) , Sorin Micu (2) , Marius Tucsnak (1, 3)

1 IECN - Institut Élie Cartan de Nancy
2 UCV - Department of Mathematics
3 CORIDA - Robust control of infinite dimensional systems and applications

We propose a new method for the approximation of exact controls of a second order infinite dimensional system with bounded input operator. The algorithm combines Russell's ''stabilizability implies controllability" principle with the Galerkin's method. The main new feature brought in by this work consists in giving precise error estimates. In order to test the efficiency of the method, we consider two illustrative examples (with the finite element approximations of the wave and the beam equations) and we describe the corresponding simulations.

Mots clés: error estimate; approximation; exact control; infinite dimensional systems

Domaines: Optimisation et contrôle [math.OC]

Nicolae Cindea, Sorin Micu, Marius Tucsnak. An approximation method for exact controls of vibrating systems. SIAM Journal on Control and Optimization, 2011, 49 (3), pp.1283-1305. ⟨10.1137/09077641X⟩. ⟨hal-00430266⟩