Heuristic dynamic programming-based learning control for discrete-time disturbed multi-agent systems

Owing to extensive applications in many fields, the synchronization problem has been widely investigated in multi-agent systems. The synchronization for multi-agent systems is a pivotal issue, which means that under the designed control policy, the output of systems or the state of each agent can be consistent with the leader. The purpose of this paper is to investigate a heuristic dynamic programming (HDP)-based learning tracking control for discrete-time multi-agent systems to achieve synchronization while considering disturbances in systems. Besides, due to the difficulty of solving the coupled Hamilton–Jacobi–Bellman equation analytically, an improved HDP learning control algorithm is proposed to realize the synchronization between the leader and all following agents, which is executed by an action-critic neural network. The action and critic neural network are utilized to learn the optimal control policy and cost function, respectively, by means of introducing an auxiliary action network. Finally, two numerical examples and a practical application of mobile robots are presented to demonstrate the control performance of the HDP-based learning control algorithm.