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A Generalization of Fundamental Stability Limits of Model Reference Adaptive Controllers in the Presence of a Class of Nonlinear Unmodeled Dynamics

机译：模型参考自适应控制器在一类非线性未定位动态存在下模型参考自适应控制器的概括

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摘要

A fundamental trade-off in the design of model reference adaptive controllers is to obtain a stable closed-loop dynamical system in the presence of not only system uncertainties but also unmodeled dynamics, which can be either linear or nonlinear. Specifically, there exist stability limits for these controllers, where the closed-loop dynamical system subject to an adaptive controller preserves stability either if there does not exist significant unmodeled dynamics or the effect of systems uncertainties is negligible. To address this problem we recently propose an adaptive control architecture to relax these stability limits for linear unmodeled system dynamics. Generalizations of the proposed adaptive control architecture are made in this paper to a broader class of unmodeled dynamics including nonlinear functions. Specifically, we utilize tools and methods from Lyapunov stability to relax stability limits for model reference adaptive controllers in the presence of nonlinear unmodeled dynamics. An illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.
机译：模型参考自适应控制器的设计中的基本折衷是在不仅存在系统不确定性的情况下获得稳定的闭环动态系统，还可以在不确定的情况下获得稳定的闭环动态系统，而且可以是无序的动态，这可以是线性的或非线性的。具体地，存在这些控制器的稳定性限制，其中经受自适应控制器的闭环动态系统如果没有存在显着的未拼接动态，则保留稳定性，或者系统不确定性的效果可以忽略不计。为了解决这个问题，我们最近提出了一种自适应控制架构，可以放宽线性未拼接系统动态的这些稳定限制。本文在本文中提出了所提出的自适应控制架构的概括，以更广泛地进行包括非线性函数的未拼件动态。具体而言，我们利用Lyapunov稳定性的工具和方法来放宽模型参考自适应控制器的稳定性限制，在非线性未拼接动态存在下。提供了说明性的数值示例以证明所提出的方法的功效。

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