Fixed-time optimal consensus for nonlinear strict-feedback multi-agent systems based on reinforcement learning and neural network observers

This paper investigates the fixed-time consensus control problem for strict-feedback multi-agent systems based on reinforcement learning. First, under the observer–critic–actor framework, neural networks are applied to the observer to address the issue of unmeasurable system states and nonlinear functions. Furthermore, based on the backstepping method, a reinforcement learning algorithm is constructed to obtain the optimal control input, which is then evaluated and optimized by the critic–actor network to derive an approximate optimal control input. Second, by constructing a Lyapunov function and utilizing the boundedness of the critic–actor network matrix trace along with Lyapunov stability theory, the fixed-time consensus of the system is proven. Finally, the effectiveness of the algorithm is verified through numerical simulations.