Adaptive Control for Nonlinear Time-Varying Systems With Unknown Control Coefficients and External Disturbances
针对具有多个未知控制系数和外部干扰的严格反馈非线性时变系统，提出一种基于新Nussbaum函数引理的自适应控制器，无需持续激励条件即可保证闭环变量有界，并进一步实现无干扰时的渐近稳定。
This article addresses the adaptive control problem for strict-feedback nonlinear time-varying systems with unknown control coefficients and external disturbances. To solve the problem of multiple unknown control coefficients, a new lemma based on a general class of Nussbaum functions rather than a specific Nussbaum function is proposed. By lumping all the time-varying parameters and control coefficients into an augmented time-varying vector, and combining the congelation of variables approach, a robust adaptive controller, without the restriction of the persistent excitation (PE) conditions, is constructed for the systems with external disturbances to guarantee the boundedness of all closed-loop variables. Then, by proper transformation, a novel adaptive control scheme is developed to achieve asymptotic stability for strict-feedback nonlinear time-varying systems without external disturbances. In addition, a tracking control method is acquired from the proposed adaptive control method. Finally, two simulations and an actual experiment demonstrate the applicability of the proposed schemes.