Sliding Mode Control Based on Reinforcement Learning for T-S Fuzzy Fractional-Order Multiagent System With Time-Varying Delays

This article researches the sliding mode control (SMC) for fuzzy fractional-order multiagent system (FOMAS) subject to time-varying delays over directed networks based on reinforcement learning (RL),
$\alpha\in(0,1).$
First, since there is information communication between an agent and another agent, a new distributed control policy
$\xi_{i}(t)$
is introduced so that the sharing of signals is implemented through RL, whose propose is to minimize the error variables with learning. Then, different from the existed papers studying normal fuzzy MASs, a new stability basis of fuzzy FOMASs with time-varying delay terms is presented to guarantee that the states of each agent eventually converge to the smallest possible domain of
$0$
using Lyapunov–Krasovskii functionals, free weight matrix, and linear matrix inequality (LMI). Furthermore, in order to provide appropriate parameters for SMC, the RL algorithm is combined with SMC strategy, and the constraints on the initial conditions of the control input
$u_i(t)$
are eliminated, so that the sliding motion satisfy the reachable condition within a finite time. Finally, to illustrate that the proposed protocol is valid, the results of the simulation and numerical examples are presented.