Coalitional predictive control: Consensus-based coalition forming with robust regulation

Abstract

This paper is concerned with the problem of controlling a system of constrained dynamic subsystems in a way that balances the performance degradation of decentralized control with the practical cost of centralized control. We propose a coalitional control scheme in which controllers of subsystems may, as the need arises, group together into coalitions and operate as a single entity. The scheme employs a robust form of distributed model predictive control for which recursive feasibility and stability are guaranteed, yet – uniquely – the reliance on robust invariant sets is merely implicit, thus enabling applicability to higher-order systems. The robust control algorithm is combined with an algorithm for coalition forming based on consensus theory and potential games; we establish conditions under which controllers reach a consensus on the sets of coalitions. The recursive feasibility and closed-loop stability of the overall time-varying coalitional control scheme are established under a sufficient dwell time, the existence of which is guaranteed.