A hybrid predictive control approach for output feedback stabilization of constrained linear systems

This work proposes a hybrid control approach, uniting bounded control with model predictive control (MPC), for the stabilization of constrained linear systems under output feedback. The approach is predicated upon the idea of switching between a bounded controller, for which a region of closed-loop stability under constraints is explicitly characterized, and a predictive controller that minimizes a quadratic performance objective subject to constraints. The state-feedback controllers are combined with a Luenberger state observer that guarantees arbitrarily fast decay of the state estimation error. Switching laws that monitor the evolution of the closed-loop state estimates are derived to orchestrate the transition between the two controllers, in a way that guarantees asymptotic closed-loop stability for all initial conditions within arbitrarily large compact subsets of the bounded controller's state-feedback stability region, provided that the observer gain is sufficiently large. The hybrid control scheme is shown to provide a safety net for the practical implementation of MPC under output feedback, by providing a fall-back controller for which there exists a priori knowledge of a large set of initial conditions for which closed-loop stability is guaranteed.