Convex Structured Controller Design
Abstract¶
We consider the problem of synthesizing optimal linear feedback policies subject to arbitrary convex constraints on the feedback matrix. This is known to be a hard problem in the usual formulations (Htwo,Hinf,LQR) and previous works have focused on characterizing classes of structural constraints that allow efficient solution through convex optimization or dynamic programming techniques. In this paper, we propose a new control objective and show that this formulation makes the problem of computing optimal linear feedback matrices convex under arbitrary convex constraints on the feedback matrix. This allows us to solve problems in decentralized control (sparsity in the feedback matrices), control with delays and variable impedance control. Although the control objective is nonstandard, we present theoretical and empirical evidence that it agrees well with standard notions of control. We also present an extension to nonlinear control affine systems. We present numerical experiments validating our approach.
Summary¶
Proposes a finite-horizon control objective that makes linear feedback synthesis convex even under arbitrary convex structure constraints on the feedback matrices. The paper is important because it sidesteps the usual nonconvexity of structured LQR, H2, and Hinf-like design by optimizing a surrogate tied to the inverse closed-loop map, enabling sparse, delayed, decentralized, and variable-impedance feedback designs with global solutions for the surrogate.