Event-Triggered Finite-Time Tracking Control for Nonlinear Systems via Immersion and Invariance Techniques

This paper researches the event-triggered forward immersion and invariant (I&I) tracking control problem for a class of strict feedback nonlinear systems. A forward I&I-based control method is developed for the tracking problem with an dynamic event-triggered mechanism. Since I&I-based method does not require the introduction of Lyapunov functions in the controller design, the design complexity is greatly reduced. Since the I&I-based method can be used to decouple the design by constructing two manifolds separately, it avoids the need of the traditional backstepping method to combine the Lyapunov function coupled design control law of radial basis function neural networks (RBFNNs). I&I adaptive technique is introduced to improve the weight update in RBFNNs. It can improve the learning performance and convergence speed of neural networks under the event-triggered mechanism. Furthermore, finite-time technique is employed to improve the error convergence time of the event-triggered forward I&I control method. For stability analysis, an event-triggered control system is denoted as a nonlinear impulsive dynamical system, and a Lyapunov theorem is then used to represent the stability of the closed-loop system without Zeno behavior. Finally, the validity of the theoretical results is illustrated by simulation examples and experiments. Note to Practitioners-The motivation of this paper is to present an event-triggered forward I&I tracking control method in finite time for a class strict feedback nonlinear system. The use of I&I technique can reduce the complexity of control method design. To reduce the computational resources, the event-triggered mechanism is introduced in the forward I&I technique. The I&I technique is introduced to construct two manifolds separately and decouple the design of the control law and the RBFNNs weight update law. Moreover, the I&I adaptive technique with the event-triggered mechanism is employed to improve the approximation effect of RBFNNs. Finally, the finitetime technique is introduced to reduce the convergence time of the tracking error under the event-triggered mechanism. This proposed method can be simply and efficiently applied in industrial applications.