Identifying Regions of Invulnerability in Multi-Agent Model Predictive Control

This paper explores the dependencies of local costs within multi-agent systems under model predictive control (MPC) actions. Specifically, we identify, for each point in each agent’s local state-space, the minimal and maximal influence of neighboring decisions. This is used to provide a bound between the global performance costs attained by noncooperative versus centralized MPC implementations, as well as to identify regions where the difference between the two is small. As such, this analysis provides suboptimality guarantees in distributed MPC schemes, particularly relevant for scenarios with reduced, and potentially dynamic, communication and coordination requirements. We illustrate the new tools in a numerical simulation of two masses coupled with springs and dampers.