Output Feedback Constrained Regulation of Linear Systems via Controlled-Invariant Sets

Design of output feedback controllers applied to the regulation problem for constrained linear discrete-time systems via set-invariance techniques is studied. Output feedback controlled-invariant (OFCI) polyhedra are used to ensure that state and input constraints are satisfied even in the presence of additive disturbances and measurement noise. Necessary and sufficient conditions for a polyhedral set to be OFCI are presented. A dynamic output feedback compensator is proposed through the construction of an OFCI set for an augmented system. Based on the measured output and on the compensator state, which constitutes an estimate of the system state, a suitable control sequence is computed via linear programming to enforce the constraints. The uncertainty on the state is progressively reduced using the contraction of an invariant set associated to the estimator. With our 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 approaches available in the literature.