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This paper investigates the adaptive fuzzy event-triggered optimized consensus tracking control problem for uncertain stochastic nonlinear multi-agent systems (MASs) with unknown dynamic and time-delay. Typically, optimal control is derived by the solution of the Hamilton-Jacobi–Bellman (HJB) equation, but it is usually challenging to solve this equation since inherent nonlinearity and unknown dynamics. Specifically, the complexity of the MASs in controller design is further exacerbated by the issue of state interdependence. To achieve optimized consensus control, the adaptive dynamic programming strategy is derived using the negative gradient of a simple positive function. As a result, the designed optimized consensus tracking control is relatively simple and can eliminate the persistence excitation (PE) assumption. The fuzzy logic systems (FLSs) are utilized to approximate the current and delayed states of unknown nonlinear functions; the identifier is proposed to estimate the stochastic multi-agent dynamic; the critic and actor FLSs are designed to evaluate control performance and execute control behavior, respectively. Furthermore, the event-triggered control (ETC) method is developed to save transmission load and communication resources. Moreover, we demonstrate that all signals for the MASs are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and that the states of the follower agents can reach consensus with the leader’s state. Finally, a numerical example is illustrated to demonstrate the effectiveness of the proposed method. Note to Practitioners—With environmental protection and energy conservation becoming dominant trends, improving efficiency is regarded as a fundamental principle in control design. In addition, MASs are widely affected by factors such as stochastic disturbance, model unknown, time-delay, and uncertain factors, which further increase the difficulty of controller design. In this work, the optimized control approach is developed to design the control strategy for MASs to achieve the control task with the minimum utilization rate of control resources. In practical application scenarios such as spacecraft control or aircraft operation, the designed optimized control scheme can not only minimize fuel consumption to complete the predetermined tasks but also eliminate the PE assumption and strong assumptions on the time-delay nonlinear functions. Furthermore, the proposed ETC strategy effectively reduces the communication resource and network transmission in practice. Therefore, the control strategy designed in this work is more easily applicable to practical engineering.
Zhang et al. (Wed,) studied this question.