High-Performance Cooperative Distributed Model Predictive Control for Linear Systems

Georgios Darivianakis, Salar Fattahi, John Lygeros, Javad Lavaei

Abstract: Distributed model predictive control (DMPC) has been proven a successful method in regulating the operation of large-scale networks of constrained dynamical systems. This paper is concerned with cooperative DMPC in which the control actions of the systems are derived by the solution of a system-wide optimization problem. To exploit the merits of distributed computation algorithms, we investigate how to approximate this system-wide optimization problem by a number of loosely coupled subproblems. In this context, the main challenge is to design appropriate terminal cost-to-go functions and invariant sets that comply with the coupling pattern of the network. The goal of this paper is to present a unified framework for the synthesis of a terminal distributed controller, cost-to-go function and invariant set based on an existing optimal centralized terminal controller. We construct an objective function for the synthesis problem, which mathematically quantifies the closeness of the given centralized and distributed control systems. This objective function is formulated using the optimizer of a robust optimization problem. Conditions for global Lyapunov stability are imposed in the synthesis problem in a way that allows the terminal cost-to-go function and invariant set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on a benchmark spring-mass-damper problem.