Fuzzy Adaptive Distributed Optimization of Uncertain Multiagent Systems With Time-Varying Delays

The distributed optimal problem is investigated in this article for uncertain nonlinear time-varying delay multiagent systems (MASs) under unknown virtual control coefficients. The primary goal is to ensure the output states converge to the ideal point of the global objective function. In comparison to the preceding results on distributed optimization, the considered MASs are subject to time delays and unknown nonlinear functions, which brought great challenges to the controller design process. To overcome this challenge, a distributed optimization algorithm is proposed via a two-stage strategy, which consists of optimization estimator design and tracking controller design. First, in the first-stage, a novel optimal signal generator is constructed by using information interaction between agents, real-time feedback value of local gradient information, so that the optimization problem is transformed into a problem of tracking control. Second, in second-stage, the fuzzy adaptive tracking control strategy is designed via backstepping technology to track the virtual signal accurately. In addition, the Lyapunov–Krasovskii functional (LKF) is applied to counteract influences brought by time-varying delays, and fuzzy logic systems are employed for handling the uncertain function in the derivative of LKF. Furthermore, an assumption is made for the time-varying delays to settle the singularity problem, which often occurs in time-delay problems. In the spirit of the convex analysis and the Barbalats lemma, the stability of the proposed algorithm is illustrated, and all variables in the closed-loop systems are bounded. Lastly, simulations are presented to validate the efficacy of the scheme.