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

Abstract

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.