Synthesis of Sparse Dynamic Structures via Semidefinite Programming

Abstract

This brief presents a systematic approach for the design of sparse dynamic output feedback control structures. A supplementary complexity cost function term is used to promote sparsity in the structure while optimizing an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance cost simultaneously. Optimization problems in which a combinatorial sparsity measure is combined with a nonlinear performance cost function are NP-hard. NP-hard problems do not have tractable solutions, requiring either a numerical solution or a relaxation into a solvable form. Relaxations will introduce conservatism, but at the same time retain stability and performance guarantees. In this brief, a new relaxation methodology is proposed, which allows the problem to be formulated as a convex semidefinite program. This is made possible via use of a new state-space form that establishes a direct relationship between the state-space and the resulting transfer function matrix parameters.