Hybrid control: a paradigm for implementing control to nonlinear systems with guaranteed stability regions

A hybrid control structure that unites bounded control with model predictive control (MPC) is proposed for the constrained stabilization of nonlinear systems. The structure consists of: 1) a finite-horizon model predictive controller, which can be linear or nonlinear, and with or without stability constraints, 2) a family of bounded nonlinear controllers for which the regions of constrained closed-loop stability are explicitly characterized, and 3) a high-level supervisor that orchestrates switching between MPC and the bounded controllers. The central idea is to embed MPC implementation within the bounded controllers´ stability regions and employ these controllers as fall-back in the event that MPC is unable to achieve closed-loop stability. Switching laws, that monitor the closed-loop state evolution under MPC, are derived to orchestrate the transitions in a way that guarantees asymptotic closed-loop stability for all initial conditions within the union of the stability regions. The proposed hybrid scheme is shown to provide a paradigm for the safe implementation of predictive control algorithms to nonlinear systems, with guaranteed stability regions. The efficacy of the proposed approach is demonstrated through a chemical reactor example.