Global adaptive finite-time stabilization with prescribed settling-time and output performance

This paper aims to solve two central challenges in finite-time control: the effective characterization of the settling time and the relationship between the constraints on system uncertainties/nonlinearities and the unbounded time-varying gains involved. The system to be investigation is characterized by high input powers, unknown control coefficients, and general nonlinearities, thereby taking an inclusive form that encompasses the existing finite-time stable systems via continuous feedback. For the system, this paper realizes finite-time stabilization via continuous adaptive control, enabling the settling-time and output performance to be prescribed in advance. First, three critical transformations are introduced, which include performance one, temporal one and state scaling one. By the transformations, the control objective of the investigated system is converted into finite-time stabilization of a certain variant to some context. Then, an adaptive controller is designed, which is typically equipped with time-varying and dynamic gains. Under the controller, the system states reach zero before a finite time instant that is strictly less than the prescribed settling time, and particularly, the system exhibits local asymptotic stability. Once the aforementioned finite time instant is reached, specific time-varying gains are immediately frozen at their current values through online monitoring. Thereafter, the frozen controller, due to the asymptotic stability, is capable of maintaining the system state at the origin. Remarkably, on the whole time horizon, the system output satisfies the performance prescribed in advance. Finally, two simulation examples show the effectiveness and practicality of the proposed controller.