Practically Time-Synchronized Command Filtered Backstepping Control of Nonlinear Systems

This article concentrates on the problem of practically time-synchronized tracking control for multi-input multi-output (MIMO) systems with unmatched nonlinearities and input saturations. Different from the existing approaches, a practically time-synchronized command filtered backstepping (CFB) control scheme is proposed. By integrating modified command filters and control signals designed with norm-normalized sign functions, the newly developed framework not only retains the advantages of the CFB control approach but also guarantees the property of time-synchronized convergence. Specifically, the “explosion of complexity” phenomenon and the influence of filtering errors are simultaneously addressed, and all components of the tracking error can achieve practically synchronous convergence to a small neighborhood of the origin in a finite time, despite the presence of unmatched nonlinearities in high-order systems. Furthermore, novel auxiliary systems are recursively embedded into each step of the time-synchronized CFB design to counteract the effect of input saturation. Rigorous theoretical analyses and comparative simulations demonstrate the rationality, effectiveness, and superiority of the proposed control scheme.