On recursive feasibility and stability of constrained output regulation

The constrained output regulation problems of discrete-time linear systems are studied under the model predictive control (MPC) framework. The unique feature of the proposed control approach lies in addressing the technical challenges related to recursive feasibility of the optimization problem and stability of the closed-loop system posed by exogenous signal estimation and estimation errors. First, the original system is transformed into a new dynamic system by means of regulator equations and disturbance observer (DO) techniques, which enables output regulation problems to be reformulated into state stabilization problems. For the constraints reconstruction, a robust positively invariant (RPI) set sequence is then skillfully designed to provide bounds for the deviations between the transformed system and its corresponding nominal system. A hierarchical control strategy is utilized that comprises two components: the first is an optimal controller designed to stabilize the nominal system with tightened constraints, while the second is a feedback controller used to restrain the deviations between the nominal and transformed systems. Constraints satisfaction can be directly verified through set operations, and the theoretical guarantees are ensured through rigorous theoretical analysis. Furthermore, the proposed framework also encompasses the output- feedback case. The numerical simulations demonstrate the effectiveness of the proposed method in addressing constrained output regulation problems, even when the exogenous signal is partially available.