A Combined Alternating Projections and Semidefinite Programming Algorithm for Low-Order Control Design

Abstract

Computational algorithms that combine convex semidefinite programming and alternating projections are proposed to solve low-order control design problems. These problems can be formulated as matrix feasibility problems described by Linear Matrix Inequalities (LMIs) and a non-convex coupling rank constraint. The proposed algorithms utilize the projections onto the LMIs, computed by interior-point methods, and the projections onto the rank constraint sets, computed analytically, to obtain feasible solutions. However, global convergence of the proposed algorithms is not guaranteed.Fixed-order stabilization, H∞, μ synthesis with constant scaling, gain-scheduling and other fixed-order control design problems can be addressed with the proposed algorithms. An example is provided to demonstrate the efficiency of the proposed methods compared to the standard alternating projections algorithm.