Distributed Economic MPC for Dynamically Coupled Systems With Stochastic Disturbances

This paper presents a distributed stochastic economic model predictive control (DSEMPC) algorithm for network interconnected systems with dynamic couplings and economic considerations. Each individual subsystem is subject to stochastic disturbances and state chance constraints. Unlike many existing methods, the proposed approach relies only on the expectation information of the disturbance and real-time estimated covariance. To transform chance constraints into the deterministic form, the Cantelli and Hoeffding inequalities are employed. Moreover, a novel robust adaptive tightened term for constraints is designed based on neighbors' reference nominal states and the estimated time-varying covariance for each subsystem. This term reduces conservativeness and decouples the dynamics, reformulating the chance constraints and ensuring recursive feasibility. The distributed control algorithm is also aimed at optimizing the economic performance whose cost function is not necessarily positive definite or quadratic in the presence of stochastic disturbance. The input-to-state stability in probability (ISSiP) of each subsystem is guaranteed through a tailored Lyapunov function in expectation form. The paper closes with a simulation of data center temperature control, highlighting the proposed results' effectiveness and the advantage of economic performance optimization.