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

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.