Predefined-time-synchronized backstepping control of strict-feedback nonlinear systems

Fixed-time-synchronized control using norm-normalized sign functions has been recently studied, where all state variables converge to the origin at the same time and the bound of the settling time is independent of the initial states. However, the existing fixed-time-synchronized control results are only applicable to second-order systems with matched nonlinearities. Thus, this article pays attention to an extension problem of time-synchronized control to high-order systems with unmatched nonlinearities. We develop a predefined-time-synchronized backstepping tracker design for multi-input multi-output strict-feedback nonlinear systems, where all output tracking errors converge to the origin at the same time, regardless of unmatched nonlinearities, and the bound of the synchronized settling time is independent of the initial errors and selected a priori. Sufficient conditions on continuously differentiable and nonsingular virtual and actual controller designs are presented for the recursive design. It is shown that the predefined-time-synchronized stability is ensured recursively and the singularity problem of the proposed tracker can be avoided. Finally, simulation comparison results with the existing fixed-time backstepping control are provided to illustrate the effectiveness of the theoretical approach.