Data-based optimal control of multiagent systems: A reinforcement learning design approach

This paper studies an optimal consensus tracking problem of heterogeneous linear multiagent systems. By introducing tracking error dynamics, the optimal tracking problem is reformulated as finding a Nash-equilibrium solution to multiplayer games, which can be done by solving associated coupled Hamilton-Jacobi equations. A data-based error estimator is designed to obtain the data-based control for the multiagent systems. Using the quadratic functional to approximate every agent's value function, we can obtain the optimal cooperative control by the input-output (I/O) ${Q}$-learning algorithm with a value iteration technique in the least-square sense. The control law solves the optimal consensus problem for multiagent systems with measured I/O information, and does not rely on the model of multiagent systems. A numerical example is provided to illustrate the effectiveness of the proposed algorithm.