Adaptive finite-time stabilization with prescribed output convergence via an integrated scheme

This article investigates global finite-time stabilization with prescribed output convergence for uncertain nonlinear systems. It is possible to achieve finite-time stabilization via continuous adaptive feedback for the systems, but the transient performance could not be prescribed for such feedback. Although funnel control is capable of tackling serious uncertainties and ensuring prescribed performance (such as convergence rate and overshoot), it alone cannot achieve (global) finite-time stabilization. To this end, we present an integrated controller to achieve the desirable stabilization, retaining the respective advantages of the above two schemes and circumventing their own disadvantages. Specifically, based on the funnel control scheme with suitable design parameters, the system output converges from any initial value to an arbitrarily adjustable region with the prescribed convergence rate before a pregiven time instant, while the system states keep bounded. The adaptive controller, in conjunction with a time-dependent function, ensures that the system output and states converge to zero in finite time, and particularly the system output with prescribed convergence rate evolves within the prespecified envelope. The effectiveness of the proposed scheme is illustrated by two simulation examples.