Adaptive Control Theory for Nonlinear Parameterized Systems and Its Application to Micro-Mechanical System

本研究的目的是寻找一种适应机制，适用于一类更一般的实际系统，这些系统的不确定性不能用未知参数线性表示。本文提出了一种新的自适应控制方法，该方法适用于任何Lipschitzian结构下的NP系统。这种思想使得自适应控制器的设计能够有效地补偿NP不确定性，因为它保证了闭环系统信号的全局有界性和在任何规定精度内的跟踪误差。结果控制器的结构很简单，因为它们是基于非线性函数的上界信息而不是基于函数的信息来设计的。该方法的一个重要特点是不要求参数集的紧性。因此，所设计的自适应控制器大大减少了计算量。此外，一类非常广泛的非线性参数化自适应控制问题，如Lipschitzian参数化，乘法参数化，分数参数化或它们的组合可以通过所提出的方法来解决。构造了机器人机械手参数不确定性补偿的自适应控制总体框架。目的是验证所提出的自适应控制技术如何实际应用于实际的动态系统。在实际的机器人操作中，NP不确定性是很常见的。机械臂关节处摩擦力的斯特里贝克效应就是一个典型的例子。这种影响会导致不希望的跟踪误差，特别是在低速跟踪任务中。然而，在机器人控制的文献中，还没有普遍解决机器人机械臂NP不确定性的自适应控制问题的结果。

Purpose of this study is to search an adaptation mechanism for a more general class of practical systems whose uncertain quantities cannot be expressed linearly with respect to unknown parameters. In this study, a novel adaptive control technique is proposed, which is applicable to any NP systems under Lipschitzian structure. This idea enables the design of adaptive controllers, which can compensate effectively for NP uncertainties in the sense that it guarantees both global boundedness of the closed-loop system signals and tracking error within any prescribed accuracies. The structures of the resulting controllers are simple since they are designed based on the information of the upper bounds for the nonlinear functions, not the functions at all. An important feature of the proposed technique is that the compactness of parametric sets is not required. Therefore, the designed adaptive controls gain a great amount of computation reduced. Also, a very broad class of nonlinearly parameterized adaptive control problems such as Lipschitzian parameterization, multiplicative parameterization, fractional parameterization or their combinations can be solved by the proposed approach.A general framework of adaptive control to compensate for parametrrc uncertainties of robot manipulators is constructed. The goal is to verify how the proposed adaptive control technique actually works with practical dynamic systems. In practical robot manipulators, NP uncertainties are common. A typical example is the Stribeck effect of frictional forces at joints of the manipulators. Such an effect results in undesired tracking errors, especially at the low-velocity tracking task. However, in the literature of robot control, there is still no result addressing the adaptive control problem for NP uncertainties of robot manipulators in a general manner.