Lyapunov-based economic model predictive control for nonlinear descriptor systems

A large number of physical applications such as electrical circuits, chemical processes and multibody systems can be accurately described by a set of differential algebraic equations (DAEs). For instance, sustainable water desalination techniques such as membrane distillation (MD) is an example of a chemical process that is described by DAEs. Optimal control strategies such as economic model predictive control (EMPC) has many operational advantages (e.g., maximizing process economics and enhancing operational safety) for chemical applications. However, constructing EMPC schemes for a general class of nonlinear DAEs systems while ensuring closed-loop stability and recursive feasibility is an open research challenge that has not been considered. Motivated by the above considerations, this note introduces a Lyapunov-based economic model predictive control (LEMPC) design that can economically operate nonlinear descriptor systems while satisfying input and states constraints. To guarantee closed-loop stability and recursive feasibility of the proposed control design, a Lyapunov-based control law is introduced to characterize the stability region at which the LEMPC can maximize the process economics. Finally, a chemical batch process modeled by nonlinear differential algebraic equations (DAEs) is utilized to demonstrate the applicability of the proposed framework.