Reference Tracking With Guaranteed Error Bound for Constrained Linear Systems

Abstract

We propose a control design for a constrained linear system to track reference signals within a given bounded error. The admissible reference signals are generated as output trajectories of a reference generator, which is a constrained linear system driven by unknown bounded inputs. The controller has to track the reference signals and to never violate a given tracking error bound, while satisfying state and input constraints, for any admissible reference. The design is based on a model predictive controller (MPC) enforcing a polyhedral robust control invariant set defined by the system and reference generator models and constraints. We describe an algorithm to compute the robust control invariant set and how to design the tracking MPC law that guarantees satisfaction of the tracking error bound and of the system constraints, and achieves persistent feasibility. We demonstrate the proposed method in two case studies.