Model-Free Containment Control of Fully Heterogeneous Linear Multiagent Systems

In this article, a model-free optimal solution is proposed for the containment control problem of fully heterogeneous discrete-time multiagent systems, in which both leaders and followers have heterogeneous dynamics. In order to make followers converge to the convex combination of leaders predefined by the users using only the collected data, a distributed control framework based on reinforcement learning (RL) for completely heterogeneous multiagent systems is developed. On the basis of the difference between follower states and target states, a local discounted performance function without considering the input index is designed for each agent to obtain the local optimal controller. The advantage of the designed performance function is that the relationship between the gain matrix of the local optimal controller and the solution of the regulation equation can be established, thus avoiding the need to solve the output regulation equation explicitly. A model-free distributed adaptive observer is designed for each follower to replace the leaders' states in optimal controller without the need to know the dynamics of leaders. Combining the optimal controller, model-free adaptive observer, and RL, the data-based optimal containment control algorithm for fully heterogeneous multiagent systems is designed and employed. Finally, numerical simulation results are given to verify the effectiveness of the proposed method.