Control Lyapunov-Barrier Function-Based Model Predictive Control of Nonlinear Systems

In this paper, we propose a Control Lyapunov-Barrier Function-based model predictive control (CLBF-MPC) method for solving the problem of stabilization of nonlinear systems with input constraint satisfaction and guaranteed safety for all times. Specifically, considering the input constraints, a constrained Control Lyapunov-Barrier Function is initially employed to design an explicit control law and characterize a set of initial conditions starting from which the solution of the nonlinear system is guaranteed to converge to the steady-state without entering a specified unsafe region in the state space. Then, the CLBF-MPC is proposed and is shown to be recursively feasible and stabilizing and to ensure the avoidance of a set of states in state-space associated with unsafe operating conditions under sample-and-hold control action implementation. Finally, we demonstrate the efficacy of the proposed CLBF-MPC method through application to a chemical process example.