Reinforcement Learning for Optimal Output Synchronization of Complex Dynamical Networks

This paper investigates the optimal output synchronization problem for a class of discrete-time heterogeneous complex dynamical networks. A novel control methodology is proposed for networks with partially unknown system dynamics. First, the distributed observers are designed for each node to reconstruct the leader’s state. Then, within the output regulation framework, a distributed dynamic compensation controller is developed for each node to achieve asymptotic output synchronization. A hybrid iterative learning algorithm is proposed to solve the optimal feedback control gains and dynamic compensation terms. The advantage of this approach lies in its independence from precise knowledge of the system matrices and its elimination of the need for an initially stabilizing controller. Finally, numerical simulations demonstrate the effectiveness and superiority of the proposed controller in achieving the asymptotical synchronization and control performance.