Sparsity-promoting optimal control of systems with invariances and symmetries

We take advantage of syntem invariance: and symmetricn to gain convexity and computational arlvantanw in regularized H-2 and H-infinity optimal control Problems. For systems with symmetric dynamics matrices, the problem of minimizing the H-2 or H-infinity performance of the closed-loop system can be cast as a convex optimization problem. Although the assumption of symmetric is restrictive, studying the symmetric component of a general system's dynamic matrices provides bounds on the H-2 and H-infinity performance of the original system. Furthermore, we show that for certain classes of system, blocks-diagnolization of the system matrices can bring the regularized optimal control problems into forms amenable to efficient computation via distributed algorithms. One such class of systems is spatially-invariant systems, whose dynamic matrices are circulant and therefore block-diagonalizable by the discrete Fourier transform. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.