Output Feedback Regulation and Constant Reference Tracking with Disturbance Rejection for Constrained Linear Systems via Controlled-Invariant Sets
Linear systems, constraints, invariant sets, output feedback, dynamic control, disturbance rejection, reference tracking.
This work is concerned with design of output feedback controllers for constrained linear discrete-time systems via set-invariance techniques. In this regard, Output-Feedback Controlled-Invariant (OFCI) polyhedra are used to ensure that state and input constraints are satisfied all time even in the presence of additive disturbances and measurement noise. Necessary and sufficient conditions for a polyhedral set to be OFCI are presented, which can be checked by the solution of a set of Linear Programming (LP) problems. Then, a dynamic output-feedback compensator (possibly nonlinear) is proposed, through the construction of an OFCI set, from a pair composed by a conditioned-invariant and a controlled-invariant polyhedron. Based on the available measurements and on the state of the compensator, which constitutes an estimate of the system state, a suitable control sequence can be computed to enforce the constraints. The uncertainty on the state is progressively reduced using information about the contraction of the conditioned-invariant set. An LP problem is formulated to compute a control action that enforces state and control constraints and minimizes, one step ahead, a guaranteed distance from the admissible states to the origin. The problem of tracking a constant reference signal in the presence of constant disturbances is also considered for which the conception of the tracking controller is motivated from the stabilizing controller. With the current approach, as illustrated through numerical examples, by embedding the estimator in the compensator structure and using the OFCI concept, it is possible to obtain solutions with larger sets
of admissible initial states and admissible initial estimation errors, compared to other approaches available in the literature.