Distributed output-feedback optimization for uncertain nonlinear multi-agent systems with unknown input delay

This paper presents distributed output-feedback optimization for uncertain high-order nonlinear multi-agent systems (MASs) subject to unknown input delay. First, appropriate auxiliary systems and Lyapunov-Krasovskii functional (LKF) are implemented to counteract the effects of unknown input delay. In addition, to address the challenges posed by nonlinear uncertainties and unmeasurable system states, a neural networks (NNs)-based state observer employing radial basis function (RBF) NNs has been developed. Subsequently, distributed optimal coordinators (DOCs) are employed to reformulate output consensus as tracking problem for MASs. In the context of actor-critic reinforcement learning (RL) architecture, distributed optimal controller is designed using RL algorithm combined with backstepping technique. Leveraging Lyapunov stability theory, it is rigorously demonstrated that the tracking error of the output relative to the optimal solution can be reduced to an arbitrarily small magnitude. Finally, simulation examples are conducted to validate the efficacy of the introduced algorithm.