Model-Free Cooperative Control for Multi-Agent Systems Using the Approximate Dynamic Programming Approach

In this paper, the approximate dynamic programming (ADP) technique is used to resolve the cooperative control problem for the completely model-free linear multi-agent systems in both continuoustime and discrete-time cases. To ensure the consensus achieved at a specified consensus speed, the modified LQR design technique is used. The sufficient condition for the consensus is derived. However, in actual applications, the precise models of the multi-agent systems cannot be easily obtained, and the nominal mathematical models are even unavailable. To overcome this difficulty, ADP-based model-free algorithms are developed to obtain the distributed protocols based on the proposed consensus design method. Moreover, the specified consensus speed can be guaranteed. Compared with the existing work, the superiority of the developed methods ensures that all the following agents synchronize to the leader with the error converging to zero instead of a bounded residual error. Two numerical examples are provided to show the effectiveness of the developed approaches.