Adaptive Event-Triggered Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Asymmetric Time-Varying Output Constraint

This paper aims to solve two intricate problems in nonlinear control: the singularity caused by driving the control to infinity at the prescribed time and the stabilization via adaptive event-triggered feedback for a class of uncertain nonlinear systems with asymmetric time-varying output constraints. The difficulty is how to dominate the implicit time in the system and the parameter error multiplied by an adaptive law without breaking the time-varying output constraint. To overcome the difficulty, we develop an event-triggered adaptive stabilizing controller comprising a time-varying scaling function and an exponential decay term, which is bounded on the whole-time interval and ensures that the states converge to the origin after entering a prescribed compact set within a prescribed finite time. Superior to the existing event-triggered schemes, the new triggered rule with a time-varying threshold guarantees that the designed controller is not only more robust against more serious uncertainties but also unifies the design in dealing with both constrained and unconstrained systems without constructing barrier functions associated with the output constraint. Finally, a practical simulation example is provided to illustrate and verify the effectiveness of the proposed approach.