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.

通过一组微分代数方程（DAE）可以准确地描述诸如电路，化学过程和多体系统之类的大量物理应用。例如，可持续的水脱盐技术（例如膜蒸馏（MD））是DAE所描述的化学过程的一个示例。诸如经济模型预测控制（EMPC）之类的最佳控制策略在化学应用中具有许多操作优势（例如，最大化过程经济性和增强操作安全性）。但是，在确保闭环稳定性和递归可行性的同时为通用非线性DAEs系统构建EMPC方案是一个尚未考虑的开放研究挑战。基于以上考虑，本说明介绍了一种基于Lyapunov的经济模型预测控制（LEMPC）设计，该设计可以经济地操作非线性描述符系统，同时满足输入和状态约束。为了保证所提出的控制设计的闭环稳定性和递归可行性，引入了基于Lyapunov的控制定律来表征LEMPC可以最大化过程经济性的稳定区域。最后，利用非线性微分代数方程（DAE）建模的化学批处理过程证明了所提出框架的适用性。引入了基于Lyapunov的控制定律，以描述LEMPC可以最大化过程经济性的稳定区域。最后，利用非线性微分代数方程（DAE）建模的化学批处理过程证明了所提出框架的适用性。引入了基于Lyapunov的控制定律，以描述LEMPC可以最大化过程经济性的稳定区域。最后，利用非线性微分代数方程（DAE）建模的化学批处理过程证明了所提出框架的适用性。