Numerical benchmarking of dual decomposition-based optimization algorithms for distributed model predictive control

This paper presents a benchmark study of dual decomposition-based distributed optimization algorithms applied to constraint-coupled model predictive control problems. These problems can be interpreted as multiple subsystems which are coupled through constraints on the availability of shared limited resources. In a dual decomposition-based framework the production and consumption of these resources can be coordinated by iteratively computing their prices and sharing them with the involved subsystems. Following a brief introduction to model predictive control different architectures and communication topologies for a distributed setting are presented. After decomposing the system-wide control problem into multiple subproblems by introducing dual variables, several distributed optimization algorithms, including the recently proposed quasi-Newton dual ascent algorithm, are discussed. Furthermore, an epigraph formulation of the bundle cuts as well as a line search strategy are proposed for the quasi-Newton dual ascent algorithm, which increase its numerical robustness and speed up its convergence compared to the previously used trust region. Finally, the quasi-Newton dual ascent algorithm is compared to the subgradient method, the bundle trust method and the alternating direction method of multipliers for a large number of benchmark problems. The used benchmark problems are publicly available on GitHub.