Adaptive Predefined-Time Stabilization: An Integrated Approach

Abstract

This paper proposes an “adaptive + time-varying” control scheme for nonlinear systems with uncertainties and high system nonlinearities, realizing the convergence before the arbitrarily predefined time. By incorporating the low-power terms into predefined-time stabilization and integrating dynamic high gains with time-varying gains, an “adaptive + time-varying” continuous controller is constructed. This continuous controller enables the system states to converge to zero before the predefined time, while effectively avoiding the singularity caused by unbounded time-varying gains in traditional control schemes. In addition, note that the system admits generic nonlinearities characterized by low-order growth rate functions. By introducing a set of different power-type parameters in the design and stability analysis, predefined-time convergence under more general system nonlinearities is achieved. A simulation example is presented to demonstrate the effectiveness of the proposed control strategy. Note to Practitioners—This work is motivated by the time-critical control in practical nonlinear systems. In practical applications, completing the tasks within a predefined time is essential. However, prescribed-time control entails unbounded time-varying gains that tend toward infinity as time $t$ approaches the predefined time $T_{p}$ . In view of this, we propose an “adaptive + time-varying” control scheme that ensures the system converges to zero within an arbitrarily prescribed time while avoiding the singularity issue. By monitoring the convergence progress online and switching the time-varying gain to a constant, the proposed method provides a more reliable implementation. Furthermore, the scheme relaxes the assumptions on system nonlinearities, making it suitable for a wider range of engineering applications subject to uncertainties and nonlinearities.