Adaptive Optimal Bipartite Consensus Control for Heterogeneous Multi-Agent Systems

In this article, a distributed adaptive optimal control method is proposed to solve the bipartite consensus problem for heterogeneous multi-agent systems. First, with a change in coordinates, the optimal bipartite consensus can be transformed into the optimal consensus problem and the optimal control law is also established. Second, a distributed state observer is designed for each agent to estimate the leader's state under the cooperate/antagonistic interaction, which is used to replace the unavailable leader's signal. Then, to find the optimal control solution adaptively, two online integral reinforcement learning algorithms, i.e., on-policy and off-policy, are developed. Based on the policy iteration in learning process, the algorithms proposed here utilize the state data of systems without requiring the complete knowledge of the leader's and agents' dynamics. It is proven that the observer is exponentially convergent, which guarantees the accuracy of solution in algorithms. Finally, two examples are given to show the validity of the proposed method.