This paper focuses on the distributed event-triggered adaptive neural resilient time-varying formation control problem for a class of multiple-input multiple-output nonlinear multi-agent systems, where all network communication links between agents are subjected to denial-of-service (DoS) attacks simultaneously. A second-order resilient time-varying formation estimator is designed to obtain the unknown leader information in DoS attack active intervals. Meanwhile, a state-triggering mechanism (STM) is designed to save system communication resources. Nevertheless, the STM can lead to virtual control laws being non-differentiable. To circumvent the problem, we first design an adaptive neural resilient formation control scheme. Then, based on the adaptive neural resilient formation control scheme, we replace continuous states with intermittent ones. By utilizing a dynamic filtering technique, an event-based adaptive neural resilient formation control scheme is designed. The key technology of control scheme design is to establish an improved first-order auxiliary system to deal with the negative impact of actuator saturation. It is proved that formation tracking errors can converge to a residual set around zero, and all signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, simulation results are presented to show the effectiveness of the control scheme.

In this paper, we propose an optimal event-triggered tracking control scheme for completely unknown nonlinear systems under the adaptive dynamic programming (ADP) framework. A data-driven model based on recurrent neural networks (RNNs) is first constructed to model the system uncertainties including the drift dynamics and the input gain matrix, and the modeling error caused by NN approximation is well eliminated through adding a compensation term in the data-driven model such that the model state can asymptotically track the system state. Apart from the traditional construction of optimal tracking controllers, in this paper, an augmented system is developed and a discounted performance function is considered to achieve the optimality. By employing the Bellman optimal principle, an event-triggered tracking Hamilton–Jacobi–Bellman (HJB) equation is then formulated. The approximate solution of the HJB equation can be obtained by virtue of a critic NN, which significantly simplifies the implementation architecture of ADP. Both the historical state data and the current state data are incorporated into the updating of the weight vector in the critic NN, in this circumstance, the persistence of excitation assumption is not needed anymore. It is strictly proven via Lyapunov stability theory that the tracking error state and the critic NN weight are uniformly ultimately bounded. Simulation results examine the validity of the design scheme.