Abstract
We propose an algorithm which combines multidirectional search (MDS) with nonsmooth optimization techniques to solve difficult problems in automatic control. Applications include static and fixed-order output feedback controller design, simultaneous stabilization, $H_2/H_\infty$-synthesis, and much else. We show how to combine direct search techniques with nonsmooth descent steps in order to obtain convergence certificates in the presence of nonsmoothness. Our technique is efficient when small and medium size controllers for plants with large state dimension are sought. Our numerical testing includes several benchmark examples. For instance, our algorithm needs 0.41\,s to compute a static output feedback stabilizing controller for the Boeing 767 flutter benchmark problem [E. E. J. Davison, IFAC Technical Committee Reports, Pergamon Press, Oxford, 1990], a system with 55 states. The first static controller without performance specifications for this system was obtained in [J. Burke, A. Lewis, and M. Overton, SIAM J. Optim., 15 (2003), pp. 751-779].
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