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

Abstract

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.