Predefined-Time Adaptive Fuzzy Distributed Optimal Output Feedback Control for Nonlinear Multiagent Systems via Reinforcement Learning

This paper investigates the adaptive fuzzy distributed optimal control problem for nonlinear multiagent systems (MASs) under the predefined-time stability theory. The addressed controlled nonlinear MASs contain unknown dynamics, immeasurable states, and input saturations. To solve unknown dynamics and immeasurable states problems, fuzzy logic systems (FLSs) are used to model the uncertain nonlinear MASs, and an adaptive fuzzy distributed state observer is designed to estimate the unknown states. Then, based on the designed state observer and differential graphical game, a predefined-time distributed optimal output feedback controller is formulated. To implement the fuzzy distributed optimal output feedback controller, a fuzzy reinforcement learning algorithm is proposed to learn the solution of the Hamilton-Jacobi-Bellman (HJB) equation, in which fuzzy logic systems are used as a critical network, and its weights adaptive laws are designed by current and historical data. It is proven that the proposed adaptive fuzzy distributed optimal controller with reinforcement learning algorithm can guarantee the closed-loop system is asymptotically stable and reaches the Nash equilibrium within the given finite-time settling time without needing the restrictive persistent excitation (PE) condition. Finally, the computer simulation results and comparison with the existing optimal control method illustrate the effectiveness of the proposed distributed optimal control scheme.