Fixed-time control design for nonlinear uncertain systems via adaptive method

This article addresses a fixed-time tracking problem of uncertain nonlinear system. Firstly, a sufficient condition for practical fixed-time stability is given. Secondly, on the basis of the sufficient condition, a novel adaptive control strategy is proposed. The designed parameter adaptive law is expressed as a nonlinear differential equation, which is different from the existing adaptive design method. Under the proposed adaptive control scheme, the system performance can be guaranteed in a fixed time, and the upper bound of the settling time is merely affected by the control design parameters, which is independent on the initial states of system. Then, based on the new established inequalities, the fixed-time stability of the closed-loop system is proved. Finally, an example is provided to illustrate the effectiveness of the main result.