Structured H control of infinite dimensional systems
We develop a novel frequency based H control method for a large class of infinite dimensional Linear TimeInvariant systems in transfer function form. A major benefit of our approach is that reduction or identification techniques are not needed, which avoids typical distortions. Our method allows to exploit both, state space or transfer function models, but also input/output frequency response data when only such are available. We aim at the design of practically useful H controllers of any convenient structure and size. We use a non smooth trust region bundle method to compute arbitrarily structured locally optimal H controllers for a frequency sampled approximation of the underlying infinite dimensional H problem in such a way that (i) exponential stability in closed loop is guaranteed, and (ii) the optimal H value of the approximation differs from the true infinite dimensional value only by a prior user specified tolerance. We demonstrate the versatility and practicality of our method on a variety of infinite dimensional H synthesis problems, including distributed and boundary control of PDEs, control of dead time and delay systems, and using a rich testing set.