Robustness Quantification and Performance Improvement in Adaptive Control Systems

这项提案中概述的研究目的有两个。首先，我们打算发展一个系统的定量理论来设计和分析鲁棒自适应控制方案。第二个目标是开发一种方法，用于研究和改进自适应控制方案的暂态性能，以及减轻不稳定的稳态行为，如猝发。上述目标涉及自适应控制领域的两个悬而未决的问题。没有现有的理论(李亚普诺夫方法、激励持续性等)能够以实际或令人满意的方式解决这些问题。缺乏这样的结果是工程师在试图将自适应控制理论的结果付诸实践时总是遇到的一个主要绊脚石。我们计划使用的方法是基于最近在稳健参数稳定性方面取得的突破(哈里托诺夫定理及其推广、参数稳定裕度的计算、参数和非结构(HoO)扰动之间的联系)和参数误差补偿方法。我们的动机是利用这些最近在鲁棒参数(非自适应)稳定性和控制方面的结果来获得自适应系统的非保守(实际有用的)稳定裕度，并开发出有效的鲁棒自适应控制设计方案。虽然鲁棒自适应控制问题比相应的非自适应控制问题困难得多，但其回报是所获得的结果可能更有用。

The aim of the research outlined in this proposal is two-fold. First, we intend to develop a systematic quantitative theory for the design and analysis of robust adaptive control schemes. The second objective is to develop a methodology for studying and improving the transient performance of adaptive control schemes, as also alleviating erratic steady state behaviour such as bursting. The objectives mentioned above relate to two of the outstanding problems in the area of adaptive control. None of the existing theory (Lyapunov approach, persistence of excitation, etc.) can solve these problems in a practical or satisfactory manner. The lack of such results is a major stumbling block that engineers invariably encounter in attempting to put the results of adaptive control theory to practice. The methods we plan to use are based on recently obtained breakthroughs in robust parametric stability (Kharitonov's Theorem and its extensions, calculation of parametric stability margins, connections between parametric and unstructured (Hoo) perturbations) and parameter- error compensation methods. We are motivated by the possibility of exploiting these recent results in robust parametric (nonadaptive) stability and control to obtain non-conservative (practically useful) stability margins for adaptive systems, and to develop effective design schemes for robust adaptive control. Though the robust adaptive control problem is much more difficult than the corresponding nonadaptive one, the payoff is that the results obtained are likely to be more useful.