Asymptotic Tracking Control of SISO Nonlinear Systems With Unknown Time-Varying Coefficients: A Global Performance Guaranteed Solution
针对一类具有严重不匹配不确定性和未知时变控制系数的单输入单输出非线性系统，提出一种全局预设性能控制方法，保证输出渐近跟踪参考轨迹且跟踪误差在预设时间内收敛到任意小的残差集。
The particular interest of this article is mainly focusing on the prescribed performance control (PPC) problem for a class of single-input single-output (SISO) nonlinear systems subject to serious mismatched uncertainties and unknown time-varying control coefficients. In contrast to most existing PPC works where the control coefficients are known or unknown while constant, the proposed control method allows multiple unknown and time-varying coefficients with nonidentical directions to be dealt with. The technical difficulty in the stability analysis arising from the multiple unknown and nonidentical directions is circumvented by proving that the effects of multiple Nussbaum-type gains in a single Lyapunov inequality can be quantified according to a newly established lemma (Lemma 2) regarding the enhanced Nussbaum functions. In addition, by resorting to a novel prescribed-time scaling function and an error transformation, it is proved that the current control method guarantees global prescribed performance in the sense that the output tracks the reference trajectory asymptotically with the tracking error converging into an arbitrarily predefined residual set at any rate of convergence within preset finite time irrespective of initial conditions and any design parameters, distinguishing itself from those semi-global results dependent on the initial conditions. The validity of the designed control scheme is confirmed by both theoretical analysis and numerical simulation.