Model-Free Distributed Consensus Control Based on Actor-Critic Framework for Discrete-Time Nonlinear Multiagent Systems

Conventionally, as the system's dynamics is known, the optimal consensus control problem relies on solving the coupled Hamilton-Jacobi-Bellman (HJB) equations. In this paper, with the unknown system dynamics being considered, a local Q-function-based adaptive dynamic programming method is put forward to deal with the optimal consensus control problem for unknown discrete-time nonlinear multiagent systems by approximating the solutions of the coupled HJB equations. First, a local Q-function is defined, which considers the local consensus error and the actions of the agent and its neighbors. Using the Q-function, it is convenient to get the derivatives with regard to the weights of the consensus control policies, even without the model of system dynamics. Then, with the defined local Q-function, a distributed policy iteration technique is developed, which is theoretically proved to be convergent to the solutions of the coupled HJB equations. An actor-critic neural network framework for implementing the developed model-free optimal consensus control method is constructed to approximate the local Q-functions and the control policies. Finally, the feasibility and effectiveness of the developed method are verified by a series of simulations.