Exact controllability of infinite dimensional hyperbolic bilinear systems

Abstract

The present study delineates the exact controllability at time T of infinite dimensional hyperbolic system with bilinear distributed controls. It consists in providing suitable controls that allow exact controllability of such a system to a target state with non null speed. It is an extension of results developed for null-speed target states Ouzahra (2014), to non null-speed target states. The approach is designed following two steps; first we give a control that ensures the approximate controllability to a target state at an intermediate time T1<T.Then, applying a feedback control over the time interval [T1,T]allows the exact controllability to such a target state at time T.A computation method is deduced and illustrative simulations are given.

Keywords

• Infinite dimensional bilinear systems
• Hyperbolic systems
• Distributed controls
• Approximate controllability
• Exact controllability