Fixed-Time Command Filtered Adaptive Backstepping Control for Uncertain Nonlinear Systems With Zero-Error Tracking

The problem of command-filter-based adaptive fixed-time tracking control is investigated for nonlinear systems with time-varying uncertain parameters and disturbances in this article. Existing fixed-time control strategies via an adaptive approach are primarily bounded-error, trajectory tracking-oriented. Different from previous results, we propose a new fixed-time stability lemma utilizing an exponential decay function. Then, by leveraging the proposed lemma and command filtered backstepping technique, a novel adaptive fixed-time control scheme is constructed, which can reduce the computational complexity and completely counteract uncertain parameters. We demonstrate that the tracking error enters a neighborhood near zero within a fixed-time and ultimately converges to zero. Furthermore, through the incorporation of a piecewise function into both the filter error compensation system and virtual control laws, the second-order derivability of virtual control laws is guaranteed, thereby ensuring the validity of the command filter. Finally, the proposed strategy's effectiveness is confirmed through simulation results.