A fundamental study of indirect adaptive control addressed towards a class of uncertain mechanical and aerospace systems is the subject of this paper. We utilize and build upon certain recent techniques within adaptive control that permit nonlinear parameterization of uncertainty, thereby amounting to a significant shift from the classical certainty equivalence methodology. Instead of the more popular direct adaptive control formulations, our focus is restricted to the indirect methods because imposing prior information on properties of physically meaningful plant parameters is convenient within this framework. For two different types of uncertainty parameterizations, namely scalar parameters and proper orthogonal matrix parameters, we present smooth, non-overparameterized (lower order), and stable adaptive control algorithms that provide improved transient performance while at the same time utilize all the available prior information on the unknown parameters. In the particular case when there exists a single scalar uncertain parameter, the most novel attribute of the proposed controller is that adaptation gets automatically frozen once the parameter estimate reaches the corresponding true value, a highly desirable feature that is clearly missing within all existing certainty equivalence adaptive control schemes. Through both analysis and simulations, we have been able to confirm that this “nice” feature amounts to having a proportional term within the parameter update law; and is in fact enabled by a crucial role played by the introduction of certain design functions that are embedded within the new controller. All technical descriptions will be further elaborated by illustrative physical examples as well as numerical simulations of the resulting closed-loop dynamics to demonstrate the potential advantages of this new approach.

中文翻译：

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自适应控制—偏离确定性等值范式

本文针对一类不确定的机械和航空系统，对间接自适应控制进行了基础研究。我们在自适应控制中利用并建立了某些最新技术，这些技术允许对不确定性进行非线性参数化，从而与传统的确定性等价方法产生了显着变化。代替更流行的直接自适应控制公式，我们的重点仅限于间接方法，因为在此框架内方便地在物理上有意义的植物参数属性上附加先验信息。对于两种不同类型的不确定性参数化，即标量参数和适当的正交矩阵参数，我们给出了平滑的，非超参数化的（低阶），稳定的自适应控制算法，可提供改进的瞬态性能，同时利用未知参数上所有可用的先验信息。在特定情况下，当存在单个标量不确定参数时，提出的控制器的最新颖的属性是，一旦参数估计值达到相应的真实值，自适应就会自动冻结，这是非常理想的功能，显然在所有现有的确定性当量中都将其丢失自适应控制方案。通过分析和模拟，我们已经能够确认此“不错”的功能等同于在参数更新定律内具有比例项。实际上，由于嵌入在新控制器中的某些设计功能的引入而发挥了至关重要的作用。