Hybrid Control: Implementing Output Feedback MPC with Guaranteed Stability Region1

In this work, a hybrid control scheme that employs switching between bounded control and model predictive control (MPC) is proposed for the output feedback stabilization of linear time-invariant systems with input constraints. Initially, we design a bounded output feedback controller for which the region of constrained closed-loop stability is explicitly characterized and an MPC controller that minimizes a given performance objective subject to constraints. Switching laws are derived to orchestrate the transition between the two controllers in a way that reconciles their respective stability and optimally properties, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid scheme is shown to provide a safety net for the practical implementation of output feedback MPC by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The proposed hybrid control approach is illustrated through a simulation example.