Robust Optimal Control Framework for Nonlinear Differential Algebraic Equations

Abstract

A vast majority of real applications as chemical processes and mechanical systems can be modeled by a set of differential algebraic equations (DAEs). For example, the well-known pendulum system is an example of a mechanical process that is described by DAEs. Optimal control algorithms such as Economic Model Predictive Control (EMPC) has many operational precedence such as maximizing process economics and enhancing physical cybersecurity for industrial applications. However, designing an EMPC paradigm for a general class of nonlinear DAEs systems while ensuring asymptotic convergence to a small neighborhood of the origin as well as recursive feasibility is an open research challenge that has not been considered. In addition, adapting to new economic considerations for optimal process operations within the scope of MPC is an interesting practical research matter. Inspired by the aforementioned considerations, this paper introduces an Economic Model Predictive Control (EMPC) paradigm that can optimize different economic cost functions for nonlinear DAE systems while meeting 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.