Non-smooth optimization for robust control of infinite-dimensional systems

We use a non-smooth trust-region method for $H_{\mathrm{\infty }}$-control of infinite-dimensional systems. Our method applies in particular to distributed and boundary control of partial differential equations. It is computationally attractive as it avoids the use of system reduction or identification. For illustration the method is applied to control a reaction-convection-diffusion system, a Van de Vusse reactor, and to a cavity flow control problem.