Event‐triggered control for a saturated nonlinear system with prescribed performance and finite‐time convergence

Abstract

Summary This paper presents an event‐triggered controller for a class of saturated uncertain nonlinear systems. We develop a performance constrained finite‐time controller to guarantee that the tracking error converges at a prescribed convergence rate and does not exceed the given maximum overshoot. A smooth function is designed to replace the absolute and signum operators in existing finite‐time controllers that lead to nondifferentiable virtual controls. Then, a novel backstepping design consisting of an adaptive law and an auxiliary system governed by a smooth switching function is developed to compensate for the uncertainty, the triggering event threshold, and the saturation constraint. Theoretical analysis demonstrates that under the proposed controller, all closed‐loop signals are bounded and the Zeno behavior is avoided. Furthermore, the tracking error will converge toward a residual set in finite time, and the prescribed transient and steady tracking performance bounds are never violated. Results from a comparative simulation study illustrate the effectiveness and advantages of the proposed method.

Event‐triggered practical finite‐time output feedback stabilization of a class of uncertain nonlinear systems

“…Relatively speaking, there are abundant research results on linear systems by using the event‐triggered control methods (see other works for example). Meanwhile, the event‐triggered control problems for nonlinear systems have also attracted extensive interest of scholars, and some exciting results have been obtained . More specifically, Li and Yang designed a model‐based event‐triggered adaptive neural network state feedback controller for uncertain nonlinear systems.…”

“…In the work of Xing et al, the event‐triggered adaptive control for uncertain nonlinear systems was investigated, in which input‐to‐state stability (ISS) assumptions are not needed by introducing compensation signals in the controller to offset event‐triggered errors. Subsequently, Zheng et al realized the event‐triggered practical finite‐time control for uncertain nonlinear systems using the traditional backstepping design consisting of an adaptive law and an auxiliary system. A rosy result of global finite‐time stability was obtained in the work of Zhang and Yang by introducing the techniques such as sign functions to completely cancel the event‐triggered errors.…”

“…Compared with the relevant results, the contributions of this article are as follows. Contrary to the state feedback control strategy adopted in other works, an event‐triggered output feedback controller is constructed for the first time to realize practical finite‐time stability for uncertain nonlinear systems based on the proper selection of Lyapunov functions and sign function techniques. Compared with the finite‐time control schemes or the existing event‐triggered control strategies, the proposed control method in this paper can simultaneously save communication resources and ensure favourable control performance. Different from the related event‐triggered output feedback control protocols, a method of dealing with the observer residuals and the event‐triggered errors is proposed rather than retaining them in the derivative of the Lyapunov functions. …”

“…Meanwhile, the event-triggered control problems for nonlinear systems have also attracted extensive interest of scholars, and some exciting results have been obtained. [19][20][21][22][23][24] More specifically, Li and Yang 19 designed a model-based event-triggered adaptive neural network state feedback controller for uncertain nonlinear systems. In the work of Xing et al, 24 the event-triggered adaptive control for uncertain nonlinear systems was investigated, in which input-to-state stability (ISS) assumptions are not needed by introducing compensation signals in the controller to offset event-triggered errors.…”

“…• Contrary to the state feedback control strategy adopted in other works, 10,19,21,22 an event-triggered output feedback controller is constructed for the first time to realize practical finite-time stability for uncertain nonlinear systems based on the proper selection of Lyapunov functions and sign function techniques. • Compared with the finite-time control schemes 6,7,26 or the existing event-triggered control strategies, 10,20,24,25,27 the proposed control method in this paper can simultaneously save communication resources and ensure favourable control performance.…”