Multi-objective model-free control based on population dynamics and cooperative games

Abstract

This work solves a model-free resource allocation problem with two objectives. These objectives represent both cooperation and competition directions. It is proposed a solution that combines a centralized cooperative game approach using the Shapley value to determine a proper partitioning of the system, and a decentralized non-cooperative game approach using the Nash equilibrium to achieve the control objective by means of both partial and local information. Furthermore, invariant set and stability analysis are discussed for the noncooperative game approach. Another contribution regarding the cooperative game approach relies on a novel and alternative way to compute the Shapley value for the chosen characteristic function. This alternative computational way is proposed in order to mitigate the commonly high computational burden issue, which is associated to the combinatorial explosion associated to the cooperative game approach.