Adaptive finite-time stabilization for uncertain nonlinear systems with unknown control coefficients

Abstract

Finite-time control owns the advantages of precision and rapidness, preferred by many applications with high performance requirements. Its realization calls for subtle treatments, e.g., the Lyapunov method with low-order terms and homogeneity with negative degree. However, the methods available for finite-time control are based on some basic exclusions and essential restrictions to system uncertainties and nonlinearities. This paper addresses for the first time unknown control coefficients without any known bound, and meanwhile extends system nonlinearities, within the framework of continuous adaptive feedback. The success is typically due to several sets of disparate powers in control design and analysis. Specifically, the nonidentical power-type parameters are introduced in high-gain dynamics, instead of an identical one in the literature, to ensure the stabilizing terms have lower powers than the terms containing uncertainties, enabling finite-time convergence. Thus an adaptive finite-time controller is achieved. New integral-type functions are exploited to make up the important Lyapunov function, which are equipped with different powers to make possible the anticipated performance analysis. The effectiveness of the proposed controller is demonstrated by a simulation example.