Sparsity-promoting optimal control of systems with invariances and symmetries

摘要

Abstract: We take advantage of system invariances and symmetries to gain convexity and computational advantage in regularized H 2 and H ∞ optimal control problems. For systems with symmetric dynamic matrices, the problem of minimizing the H 2 or H ∞ performance of the closed-loop system can be cast as a convex optimization problem. Although the assumption of symmetry is restrictive, studying the symmetric component of a general system’s dynamic matrices provides bounds on the H 2 and H ∞ performance of the original system. Furthermore, we show that for certain classes of systems, block-diagonalization 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.