Distributed control of networked systems with coupling constraints

Abstract This paper proposes algorithms for the distributed solution of control problems for networked systems with coupling constraints. This type of problem is practically relevant, e. g., for subsystems which share common resources, or need to go through a bottleneck, while considering non-convex state constraints. Centralized solution schemes, which typically first cast the non-convexities into mixed-integer formulations that are then solved by mixed-integer programming, suffer from high computational complexity for larger numbers of subsystems. The distributed solution proposed in this paper decomposes the centralized problem into a set of small subproblems to be solved in parallel. By iterating over the subproblems and exchanging information either among all subsystems, or within subsets selected by a coordinator, locally optimal solutions of the global problem are determined. The paper shows for two instances of distributed algorithms that feasibility as well as continuous cost reduction over the iterations up to termination can be guaranteed, while the solutions times are considerably shorter than for the centralized problem. These properties are illustrated for a multi-vehicle motion problem.