Data-Driven Distributed Model Predictive Control of Continuous Nonlinear Systems with Gaussian Process

Abstract

This work explores the design of distributed model predictive control (DMPC) systems using Gaussian process (GP) models to predict the nonlinear dynamic behavior for nonlinear processes with unknown dynamics. Specifically, the DMPC is designed and analyzed concerning closed-loop stability and performance properties based on the Lyapunov techniques. First, the GP model used in the DMPC is developed and updated in a distributed manner where each subsystem only considers its physically interacted states except its own states to get a sufficiently accurate model with a relatively smaller data set and achieve efficient real-time computation time. Then, a Lyapunov constraint, which is related to the model mismatch quantified by the GP model, is developed to guarantee the stability of the proposed DMPC system at a given confidence level. Meanwhile, a mechanism for triggering the update of the GP’s data set and the Lyapunov constraint is proposed that keeps the recursive feasibility of the DMPC system and the improvement of the steady-state performance. Finally, using an ethylbenzene production process as an example, the simulation results demonstrate the effectiveness of the proposed DMPC system.