Fast and scalable constrained reference tracking for discrete-time linear systems

This paper considers the synthesis of tracking control laws for discrete-time linear systems. A two-step approach that results in a sequence of quadratic contractive sets is proposed. Firstly, the quadratic sets are obtained by maximizing the size of the sets. Then, secondly, a conic partition is employed to construct continuous conewise linear control laws for each quadratic set while optimizing performance. Furthermore, a set-theoretic method is employed to extend the stabilizing law for the tracking control problem. As a result it yields scalable off-line computation of the control law. Moreover, this approach provides stability guarantees and constraints satisfaction. The effectiveness of the approach is demonstrated using an illustrative example.