Prespecifiable fixed-time control for a class of uncertain nonlinear systems in strict-feedback form

In this paper, we investigate the prespecifiable fixed-time control problem for a class of uncertain nonlinear systems in strict-feedback form, where the settling (convergence) time is not only bounded but also user-assignable in advance. One of the salient features of the proposed method lies in the fact that it makes it possible to achieve any practically allowable settling time by using a simple and effective control parameter selection recipe. Both fixed-time stabilization and fixed-time tracking are considered for uncertain strict-feedback systems. Firstly, by adding exponential state feedback and using fractional power integration as Lyapunov function candidate, a global stabilizing control strategy is developed. It is proved that all the system states converge to zero within prespecified fixed-time with continuous and bounded control action. Secondly, under more general uncertain nonlinearities and external disturbances, an adaptive fixed-time controller is derived such that the tracking error converges to a small neighborhood of zero within preassigned time. Theoretical results are also illustrated and supported by simulation studies.