Predefined‐time backstepping control for a nonlinear strict‐feedback system

Abstract Two novel predefined‐time control algorithms for a nonlinear strict‐feedback system are proposed in this short communication. It is required that the upper bound of system convergence time is exactly a positive constant parameter in each algorithm, and it can be selected arbitrarily by users. Composite state tracking errors are introduced to the backstepping design process by using some novel smooth time‐varying tuning functions. In order to address the problem of explosion of complexity in the first algorithm, the second algorithm extends the predefined‐time control strategy to a dynamic surface control (DSC) case. Furthermore, the proposed predefined‐time DSC algorithm can guarantee global stability rather than semi‐global stability for the closed‐loop system compared with traditional DSC algorithms. Simulation results show the effectiveness of the two control schemes.