A game theoretical formulation for distributed optimization problems

The focus of this paper is to develop a theoretical framework for analysis and design of distributed optimization problem in multi-agent systems by using the language of game theory and cooperative control methodology. In the framework, a piecewise-constant and binary-valued matrix in the cooperative control theory is introduced to describe the sensing/communication among agents and to cope with the practical situations where the information sharing may be in a distributed, dynamically changing and local manner. Based on information acquisition/communication model, state based ordinal potential game is designed to capture the optimal solution to distributed optimization problems in multi-agent systems by appropriately specifying local objective function for each individual decision maker. It is worth noting that the proposed analysis and design methodology has the advantages that the resulted equilibriums are capable of solving the distributed optimization problems even if the corresponding communication topologies is local, time-varying and intermittent. Meanwhile, the minimal requirement for the communication among the agents is provided to ensure the global objective is desirable under the new framework.