A new adaptive designated-time stabilizing strategy for uncertain time-varying nonlinear systems

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.