Structured controller synthesis through block-diagonal factorization and parameter space optimization

Abstract

Constraints on the feedback structure arise in many control systems due to implementing cost, hardware limitations and operational reliability. The parameter space method aims to solve the robust structured controller design problems based on a convex reformulation technique. Despite its attractiveness, the structural constraints are limited to be either decentralized or linear dependence among entries within the same row or column in the current literature. And the global optimal solution is yet to be guaranteed, since a non-convex constraint is introduced in the parameter space after reformulating it as the output feedback synthesis problem. In this paper, we extend the parameter space method to a more generalized structured optimal control problem, such that the linear dependence can occur among its arbitrary entries. A bilinear factorization to the feedback gain matrix is proposed by a special Kronecker product decomposition. Subsequently, an equivalent transformation is proposed to convert this structured control design problem to a controller synthesis problem under decentralized full-state feedback. Thereby, the prior non-convex constraint in the parameter space is removed and the globally optimal structured controller is synthesized by convex programming. Examples such as integrated design and formation control demonstrate its practical appeals.