Reinforcement learning-based optimized multi-agent finite-time optimal synchronisation control and its application to the harmonic oscillator

This paper investigates the finite-time optimal synchronisation problem for leader-follower multi-agent systems and its application to the harmonic oscillator models. Neural networks are introduced to fit the nonlinear terms of multi-agent systems due to the existence of unknown dynamics. In our designed framework, by modelling each agent as a resonator, their interactions and environment can be shaped as a networked system. In pursuit of synchronized actions among adjacent agents, the actor-critic reinforcement learning algorithm is implemented. To simplify the algorithm and eliminate persistent incentive conditions simultaneously, gradient descent method is applied to a novel positive function. Furthermore, a finite-time control strategy, based on reinforcement learning algorithms, has been devised to ensure that the system not only achieves control objectives within finite time but also minimizes the energy consumption in the process. Finally, the validity of the theoretical method is proven by the Lyapunov stability theory and numerical simulation.