Fixed-Time Command Filtered Adaptive Backstepping Control for Uncertain Nonlinear Systems With Zero-Error Tracking
针对含时变不确定参数和扰动的非线性系统，提出一种基于新固定时间稳定性引理和指令滤波反步法的自适应控制方案，实现跟踪误差在固定时间内收敛到零，并降低计算复杂度。
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.