AN EFFICIENT DECOMPOSITION-BASED FORMULATION FOR ROBUST CONTROL WITH CONSTRAINTS

Abstract

This paper is concerned with the development of an efficient computational solution method for control of linear discrete-time systems subject to bounded disturbances with mixed polytopic constraints on the states and inputs. It is shown that the non-convex problem of computing an optimal affine state feedback control policy can be solved through reparameterization to an equivalent convex problem, and that if the disturbance set is the linear map of a hypercube, then this problem may be decomposed into a coupled set of finite horizon control problems. If the problem involves the minimization of a quadratic cost, then this yields a highly structured quadratic program in a tractable number of variables, which can be solved with great efficiency.