Lyapunov-Based EMPC: Closed-Loop Stability, Robustness, and Performance

Abstract

In this chapter, various Lyapunov-based economic model predictive control (LEMPC) designs are developed, which are capable of optimizing closed-loop performance with respect to general economic considerations for nonlinear systems. Numerous issues arising in the context of chemical process control are considered including closed-loop stability, robustness, closed-loop performance, asynchronous and delayed sampling, and explicitly time-varying economic cost functions. Closed-loop stability, in the sense of boundedness of the closed-loop state, under the LEMPC designs is analyzed. Additionally, when desirable, the LEMPC designs may be used to enforce convergence of the closed-loop state to steady-state. Under a specific terminal constraint design, the closed-loop system under the resulting LEMPC scheme is shown to achieve at least as good closed-loop performance as that achieved under an explicit stabilizing controller. The LEMPC approaches are demonstrated with chemical process examples.