Delay-dependent recursive feasibility based switched model predictive control for nonlinear systems

Abstract

This paper presents a coordinated design of a model predictive controller (MPC) and switching law for delayed nonlinear switched systems with Lipschitz property. The article derives delay-dependent recursive feasibility constraints to handle disturbances in a polytopic form and incorporates them into the optimization problem. The control gain at each step is determined to ensure the feasibility of the optimization problem during the execution time of each sub-system. Additionally, constraints related to the cost function and H$\infty$ performance conditions are introduced in the developed linear matrix inequality problem to minimize the cost function with an infinite predictive horizon and guarantee controller robustness against unknown constant delays. The coordinated design of the MPC and switching law is achieved using the multiple Lyapunov–Krasovskii functional, which reduces the strictness of the controller constraints compared to the switched Lyapunov–Krasovskii functional. However, it imposes a dwell-time limitation on the switching law. By adopting the PDT structure, the dwell-time limitation is reduced compared to common structures. To evaluate the proposed design, it is applied to a water pollution system, and its performance is assessed. The results demonstrate superior performance compared to previous works.