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.

This paper explores the adaptive designated-time stabilizing strategy for a class of uncertain time-varying nonlinear systems. The inspiration is driven by two challenging issues that remain unsolved in the field of prescribed-time stabilization: i) the singularity induced by infinity control magnitudes at the prescribed time instant and ii) the incapability of driving state behavior after the prescribed time. To tackle the challenges, we formulate a hybrid stabilizing controller by utilizing both the state scaling technique and a finite-time stabilizing process, which is bounded on the whole-time horizon and guarantees the existence of the solutions of the closed-loop system. Superior to the current prescribed-time stabilization results, the proposed strategy is not only able to ensure that the states of the closed-loop system converge to a compact set within a designated time and belongs to the set afterward, and enjoys finite-time convergence ultimately, but also manipulate intricate dynamics and parameter uncertainties effectively. Finally, simulation examples are given to demonstrate the validity of the proposed strategy.

This article aims to solve a challenging problem in tracking control of the wind turbines' rotor speed: achieving the tracking of the speed for the reference signal within a prescribed time so as to guarantee that turbines capture the maximum wind power. The difficulty is how to make the sign of the tracking error invariable on the whole time-horizon while keeping the difference between the high-speed shaft angle and the low one bounded. Based on barrier functions constructed with constrained boundaries and the reference signal, we develop a novel continuous feedback controller by introducing a time-varying function associated with the prescribed time. Superior to the existing tracking results of wind turbines, the presented strategy is capable of driving the speed to track the desired signal within a prescribed time and obtaining the guaranteed performance, which is characterized by nonovershooting tracking error and inviolate time-varying asymmetric output constraints. Finally, experiments by MATLAB and hardware-in-the-loop are conducted to exhibit the effectiveness/advantages of the developed technique.

This article explores the problem of prescribed-time stabilization for a class of high-order polynomial nonlinear systems with unknown time-varying nonlinearities. The key technique behind the proposed strategy involves fixing the time-varying components to their bounded values before the prescribed time and establishing a new lemma to suppress the time-varying continuous functions in the investigated system. We design a continuous bounded feedback controller to address the singularities induced by infinite control gains at the prescribed time and to suppress the implicit effects of time variations. Superior to the existing prescribed-time stabilization results, our strategy achieves the states’ convergence within the prescribed-time and the nontruncated run of controller simultaneously. We employ the wing rock motion to demonstrate the practicality and superiority of the developed strategies.