A game theory approach to multi-agent team cooperation

The main goal of this work is to design a team of agents that can accomplish consensus over a common value for the agents´ output in a cooperative manner. First, a semi-decentralized optimal control strategy introduced recently by the authors is utilized which is based on minimization of individual costs using local information. Cooperative game theory is then used to ensure team cooperation by considering a combination of individual costs as a team cost function. Minimization of this cost function results in a set of Pareto-efficient solutions. The choice of Nash-bargaining solution among the set of Pareto-efficient solutions guarantees the minimum individual cost. The Nash-bargaining solution is obtained by maximizing the product of the difference between the costs achieved through the optimal control strategy and the one obtained through the Pareto-efficient solution. The latter solution results in a lower cost for each agent at the expense of requiring full information set. To avoid this drawback additional constraints are added to the structure of the controller by using the linear matrix inequality (LMI) formulation of the minimization problem. Consequently, although the controller is designed to minimize a unique team cost function, it only uses the available information set for each agent.