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.

This paper investigates the problem of unknown virtual control directions in a state-quantized adaptive recursive control design for a class of arbitrarily switched uncertain pure-feedback nonlinear systems in a band-limited network. State quantization is considered for state feedback control in a bandlimited network. The primary contribution of this study is to provide a quantized state feedback adaptive control strategy to address the unknown control direction and arbitrarily switched nonaffine nonlinearities. Herein, a coupling problem between Nussbaum functions and quantization errors caused by quantized state feedback control laws is considered in the Lyapunov-based design and stability analysis. A statequantized adaptive recursive control scheme using the function approximation is constructed without a priori knowledge of the signs of the control gain functions, where the estimated parameters and Nussbaumtype functions are adaptively updated via quantized states. Theoretical lemmas are derived to show that the adaptive parameters and quantization errors of the closed-loop signals are bounded using the proposed control scheme. The boundedness of the closed-loop signals and the convergence of tracking error to a neighborhood of the origin are proved using the common Lyapunov function approach. Two simulation examples are shown to illustrate the effectiveness of the proposed theoretical result.