Distributed Economic MPC for Dynamically Coupled Linear Systems: A Lyapunov-Based Approach

Abstract

This article develops a distributed economic model predictive control (EMPC) method which is applied in a group of interconnected linear subsystems subject to unknown bounded disturbances. Multiple subsystems are coupled through the dynamics, and the control objective is to optimize some general performance criteria of the whole system which may take economic considerations into account. First, a two operation modes EMPC optimization problem is formulated, which incorporates the constraints derived from the Lyapunov technique. In the first mode, each subsystem focuses on the optimization of the economic performance while maintaining the state in a certain region. In the second mode, the system states are steered to a neighborhood of a steady state by making use of the Lyapunov-based constraints. Furthermore, a consensus alternating direction method of multipliers (ADMM) is adopted to solve the model predictive control optimization problems with a coupled predicted model constraint in a distributed way. By introducing consensus constraints, the resulting local optimization problem does not depend on real-time optimal solutions from neighboring subsystems and allows subsystems to solve it in parallel. Moreover, the closed-loop system is ensured to be input-to-state stable (ISS) with respect to the disturbances. To demonstrate the effectiveness of the algorithm, we conduct numerical simulations on a thermal power interconnected system.