Event-triggered control of nonlinear systems with input saturation and time-varying control gain

In this paper, an event-triggered adaptive control law is proposed by backstepping for a class of nonlinear systems with unknown saturation input. It also considers uncertain constant parameters and unknown time-varying input gains in the system. The analysis of the relationship between the continuous input signal before triggering and the discrete signal after triggering, transformed by a saturated actuator, is key to the controller design. Based on this, a new smooth function is constructed to approximate asymmetric saturation. The shortcomings of the auxiliary signal method and fuzzy approximation method can be overcome by this approximation. The approximation error is analysed in conjunction with the uncertainty introduced by the unknown time-varying input gains. The Nussbaum function is introduced to compensate for the impact of this combined uncertainty. All signals remain bounded by the proposed control scheme in the closed-loop system and simulation results can also prove the effectiveness of this proposed controller.