Fixed‐time stabilization of uncertain strict‐feedback nonlinear systems via a bi‐limit–like strategy

Abstract

Summary This paper concerns the fixed‐time stabilization problem for uncertain strict‐feedback nonlinear systems. Generally, the so‐called fixed‐time stabilization is an extended concept of global finite‐time stabilization. By using fixed‐time controller, the convergence time of the closed‐loop system can be pre‐set by adjusting design parameters, which has more practical application values. The idea of bi‐limit homogeneity has been introduced to design the fixed‐time controller with two terms, whose orders are tuning by a bi‐limit–like strategy. That is the orders of the two terms are less than 1 and more than 1, respectively. Meanwhile, by utilizing power integral terms in the controller, the problem arising from the growth rates of uncertain nonlinear functions can also be solved. Based on appropriate Lyapunov function and backstepping technology, the parameters of the controller are finally determined, and the developed controller ensures the stabilization of system within a fixed time. Stability analysis and simulation results are respectively given to verify the effectiveness of the proposed method.

Fixed-time stabilization for lower-triangular nonlinear systems under the p-normal form

“…Through adopting the common Lyapunov functional (LF) method, the FTS for a series of switched NLSs in the p -normal form was derived in Gao et al (2019). FTS of uncertain NLSs with strict-feedback via a bi-limit-like technique was studied in Yang and Ye (2018). FTS of neural network has been addressed in Michalak and Nowakowski (2021).…”

Fixed‐time stabilization for a class of nonlinear time‐delay systems

“…The time‐varying feedback stabilization problem with fixed‐time boundary for constant parameter reaction‐diffusion systems was considered in 34 . Fixed‐time control problem of uncertain nonlinear strict feedback systems was proposed in 35 . FTS for a class of higher order nonlinear systems was considered in 36 .…”