Nonsmooth Optimization for Multidisk H∞ Synthesis

We discuss output feedback control design with multiple performance specifications, each measured in a weighted H∞-norm. The multidisk design problem consists in finding a stabilizing output feedback controller which minimizes the different performance specifications simultaneously using a worst case strategy. This is less conservative than existing approaches, but difficult to solve algorithmically due to inherent nonsmoothness and nonconvexity. We present a nonsmooth optimization method suited for the multidisk problem and more generally, for programs where the maximum of an infinite family of nonconvex maximum eigenvalue functions is minimized. The method is shown to perform well on a control problem for a helicopter at hover.