Computational Aspects of Distributed Optimization in Model Predictive Control

This paper presents a systematic computational study on the performance of distributed optimization in model predictive control (MPC). We consider networks of dynamically coupled systems, which are subject to input and state constraints. The resulting MPC problem is structured according to the system's dynamics, which makes the problem suitable for distributed optimization. The influence of fundamental aspects of distributed dynamic systems on the performance of two particular distributed optimization methods is systematically analyzed. The methods considered are dual decomposition based on fast gradient updates (DDFG) and the alternating direction method of multipliers (ADMM), while the aspects analyzed are coupling strength, stability, initial state, coupling topology and network size. The methods are found to be sensitive to coupling strength and stability, but relatively insensitive to initial state and topology. Moreover, they scale well with the number of subsystems in the network.