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The problem of finite-time adaptive tracking control against event-trigger error is investigated in this article for a type of uncertain nonlinear systems. By fusing the techniques of command filter backstepping technical and event-triggered control (ETC), an adaptive event-triggered design method is proposed to construct the controller, under which the effect of event-triggered error can be compensated completely. Moreover, the proposed controller can increase robustness against uncertainties and event error in the backstepping design framework. In particular, we establish the finite-time convergence condition under which the tracking error asymptotically converges to zero in finite time with the aid of a scaling function. Detailed and rigorous stability proofs are given by making use of the improved finite time stability criterion. Two simulation examples are provided to exhibit the validity of the designed adaptive ETC approach.

This brief addresses the adaptive neural asymptotic tracking issue for uncertain non-strict feedback systems subject to full-state constraints. By introducing the significant nonlinear transformed function (NTF), the command filtered technology, and the boundary estimation method into control design, a novel command filtered backstepping adaptive controller is proposed. The proposed control scheme is able to not only deal with full-state constraints but also avoid the ``explosion of complexity'' issue. By means of a Lyapunov stability analysis, we prove that: 1) the tracking error asymptotically converges to zero; 2) all the variables in the controlled systems are bounded; and 3) all the states are constrained in the asymmetric predefined sets. Finally, a numerical simulation is used to demonstrate the validity of the proposed algorithm.

This article systematically addresses the distributed event-triggered containment control issues for multiagent systems subjected to unknown nonlinearities and external disturbances over a directed communication topology. Novel composite distributed adaptive neural network (NN) event-triggering conditions and event-triggered controller are raised meanwhile. Furthermore, the designed event-triggered controller is updated in an aperiodic way at the moment of event sampling, which saves the computation, resources, and transmission load. On the basis of the NN-based adaptive control techniques and event-triggered control strategies, the uniform ultimate bounded containment control can be achieved. In addition, the Zeno behavior is proven to be excluded. Simulation is presented to testify the effectiveness and advantages of the presented distributed containment control scheme.

This paper is concerned with the adaptive event-triggered control problem for a class of pure-feedback nonlinear systems. Unlike the existing results where the control execution is periodic, the new proposed scheme updates the controller and the neural network weights only when desired control specifications cannot be guaranteed. Clearly, this can largely reduce the amount of transmission data. Besides, since the event-trigger error is discontinuous because of the event-triggering mechanism, the stability analysis in the classical sense may not be guaranteed. To solve this problem, we formulate the event-triggered network control systems as a nonlinear impulsive dynamical system, and a novel Lyapunov theorem is used to show the stability properties of the closed-loop systems. Finally, two simulation examples are given to illustrate the effectiveness of the theoretical results.

This paper is concerned with the simultaneous design of a neural network (NN)-based adaptive control law and an event-triggering condition for a class of strict feedback nonlinear discrete-time systems. The stability and tracking performance of the closed-loop network control system under the event-triggering strategy is formally proven based on the Lyapunov theory in a hybrid framework. The proposed Lyapunov formulation yields an event-triggered algorithm to update the control input and NN weights based on conditions involving the closed-loop state. Different from the existing traditional NN control schemes where the feedback signals are transmitted and executed periodically, the feedback signals are transmitted and executed only when the event-trigger error exceeds the specified threshold, which can largely reduce the communication load. The effectiveness of the approach is evaluated through a simulation example.

This paper is concerned with the adaptive event-triggered control problem of nonlinear continuous-time systems in strict-feedback form. By using the event-sampled neural network (NN) to approximate the unknown nonlinear function, an adaptive model and an associated event-triggered controller are designed by exploiting the backstepping method. In the proposed method, the feedback signals and the NN weights are aperiodically updated only when the event-triggered condition is violated. A positive lower bound on the minimum intersample time is guaranteed to avoid accumulation point. The closed-loop stability of the resulting nonlinear impulsive dynamical system is rigorously proved via Lyapunov analysis under an adaptive event sampling condition. In comparing with the traditional adaptive backstepping design with a fixed sample period, the event-triggered method samples the state and updates the NN weights only when it is necessary. Therefore, the number of transmissions can be significantly reduced. Finally, two simulation examples are presented to show the effectiveness of the proposed control method.