Abstract
Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS) is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.
Highlights
Since the concept of finite-time stability was introduced in [1], many efforts have been made to study the problem of finitetime stabilization because of faster convergence rates, higher accuracies, and better disturbance rejection properties
Based on the finite-time stability theorem in [2,3,4], some finite-time stabilization results have been achieved by combining finitetime stability with backstepping design method, for example, [5,6,7,8,9] and the references therein
The restrictive condition was relaxed by [12], in which all the states in the bounding condition were allowed to be of both low order and high order
Summary
Since the concept of finite-time stability was introduced in [1], many efforts have been made to study the problem of finitetime stabilization because of faster convergence rates, higher accuracies, and better disturbance rejection properties. More attention of finite-time stability has been focused on a family of high-order nonlinear systems of the form ẋi (t) = xip+i1 (t) + φi (x1 (t) , . For system (1), when d is known, [10, 11] studied finitetime stability, where the order of state xj The restrictive condition was relaxed by [12], in which all the states in the bounding condition were allowed to be of both low order and high order. It is well known that adaptive technique is an effective way to deal with control problem of nonlinear systems with parametric uncertainty. Reference [13] developed a continuous adaptive finite-time controller with the bounding condition of φi being an order equal to 1. There is no dynamic uncertainty considered by these papers
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