Uniting bounded control and MPC for stabilization of constrained linear systems

In this work, a hybrid control scheme uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated on the idea of switching between a Lyapunov-based bounded nonlinear controller, for which a region of closed-loop stability under constraints is explicitly characterized, and a model predictive controller that minimizes a quadratic performance objective subject to constraints. Switching laws, that monitor the evolution of the closed-loop trajectory under MPC, within the stability region, and place appropriate restrictions on any concomitant growth of the Lyapunov function, are derived to orchestrate the transition between the two controllers, in a way that guarantees asymptotic closed-loop stability for all initial conditions within the stability region. The hybrid scheme is shown to provide a computationally efficient means for the implementation of MPC by providing, through off-line computations, a priori knowledge of a set of initial conditions for which closed-loop stability is guaranteed. The proposed approach is illustrated through a simulation example.