Economic optimization and predictive control for nonlinear systems using Lyapunov based nonlinear cost function design

Abstract

Optimal control of physical processes depends on the formulation of objective functions and contemplation of appropriate predictive control. In this article, we propose a new framework, to blend the concepts of the Lyapunov-based economic model predictive control (Ly-EMPC) scheme with the novel cost-efficient profit function design. Furthermore, Lyapunov’s stability criteria is employed to verify the existence of duality and optimality for the designed economic stage costs. This method differs from the existing EMPC techniques by implementing Lagrange multipliers in the rotated cost function as a measure of stability. The closed-loop performance using the regularized Ly-EMPC is validated against a standard tracking objective-based nonlinear MPC for three benchmark examples through an econometrics gauge factor. Interestingly, in contrast to tracking NMPC, the proposed Ly-EMPC scheme excels in economic performance, while the formation of nonlinear economic stage cost is conceptually simpler, novel, and practically profitable.