具有未知函数非线性系统的全局渐近稳定控制

Global asymptotic stability control for nonlinear systems with unknown functions

中文关键词  非线性系统  渐近稳定  反步法  状态反馈

英文关键词  nonlinear systems  asymptotic stability  backstepping  state feedback

中文摘要

      本文讨论了一类具有未知函数和未知控制方向非线性系统的全局渐近稳定问题. 通过提出一个引理处理 未知函数问题, 从而得到了一种基于反步法和Nussbaum增益技术的全局渐近稳定控制算法. 与逼近方法处理未知 函数的算法相比, 本文提出的算法解决了非线性系统的全局渐近稳定问题; 与现存解决非线性系统的全局渐近稳 定控制算法相比, 本文避免了使用未知函数的假设条件, 因此降低了保守性. 值得一提的是本文的算法也解决了反 步法的“微分爆炸”问题, 因此所提出的控制方案不仅仅得到了全局渐近稳定控制方案, 而且降低了计算的复杂性. 最后, 将该方案应用到刚性单链杆机械手系统中, 仿真结果验证了其有效性.

英文摘要

      In this paper, the global asymptotic stability of a class of nonlinear systems with unknown functions and unknown control directions is discussed. A lemma is proposed to deal with the unknown functions problem, and a global asymptotic stability control algorithm based on the backstepping and Nussbaum gain technology is obtained. Compared with the algorithms dealing with unknown functions by approximation method, the algorithm proposed in this paper solves the problem of global asymptotic stability of nonlinear systems. Compared with the existing global asymptotic stability control algorithms for nonlinear systems, this paper avoids the assumptions of unknown functions, so the method in this paper reduces the conservatism. It is worth mentioning that the algorithm in this paper also solves the “explosion of terms” problem of backstepping. Therefore, the algorithm in this paper not only obtains the global asymptotic stability control scheme, but also has simple calculation. Finally, the algorithm is applied to the rigid single link manipulator system, and the simulation results verify the effectiveness of the control scheme.