Small-gain based distributed Model Predictive Control of nonlinear continuous processes

• Published in: Chemical engineering research & design Vol. 223; pp. 177 - 184
• Main Authors: Zheng, Yi, Liu, Qibo, Zhao, Qingchun, Wang, Yanye, Li, Shaoyuan
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2025
• Subjects: Distributed systems; Model Predictive Control; Nonlinear processes; Small-gain theorem; Small-gain theorem; Nonlinear processes; Distributed systems; Model Predictive Control
• ISSN: 0263-8762
• DOI: 10.1016/j.cherd.2025.09.026

This paper proposes a distributed Model Predictive Control (MPC) for continuous nonlinear systems composed of interconnected subsystems. The proposed distributed MPC builds upon Lyapunov-based MPC by incorporating the small-gain theorem to ensure stability. Specifically, a stability constraint is designed to limit the derivative of the subsystem-based ISS-Lyapunov function of each subsystem under the action of the designed subsystem-based MPC to be less than that under an existing controller. Sufficient conditions are derived to ensure that the states of the closed-loop system converge to a small region around the equilibrium under the proposed method. The design of a certain subsystem-based MPC only relies on its dynamics and the resulting gain relationship with its associated subsystems, and each subsystem-based MPC operates with neighbor-to-neighbor communication. These keep the structural flexibility of the control system. The designed DMPC does not require that all subsystem-based Lyapunov functions decrease simultaneously. This positively impacts the performance of the entire system. Finally, an application of the proposed method to a chemical process demonstrates its effectiveness. •A DMPC design based on the small-gain theorem and the Lyapunov-based techniques.•Designed in a distributed manner, only requiring knowledge of interacting subsystems.•Providing potential for performance improvement.•Communicating with neighboring subsystems.•Sufficient conditions for the convergence of the entire system are provided.