GrHDP Solution for Optimal Consensus Control of Multiagent Discrete-Time Systems

This paper develops a new online learning consensus control scheme for multiagent discrete-time systems by goal representation heuristic dynamic programming (GrHDP) techniques. The agents in the whole system are interacted with each other through a communication graph structure. Therefore, each agent can only receive the information from itself and its neighbors. Our goal is to design the GrHDP method to achieve consensus control which makes all the agents track the desired dynamics and simultaneously makes the performance indices reach Nash equilibrium. The new local internal reinforcement signals and local performance indices are provided for each agent and the corresponding distributed control laws are designed. Then, GrHDP algorithm is developed to solve the multiagent consensus control problem with the proof of convergence. It is shown that the designed local internal reinforcement signals are bounded signals and the local performance indices can monotonically converge to their optimal values. Moreover, the desired distributed control laws can also achieve optimal. Two simulation studies, including one with four agents and another with ten agents, are applied to validate the theoretical analysis and also demonstrate the effectiveness of the proposed method.