Robust Adaptive Control Based on Kharitonov Theory and Its Extensions

1995年8月2日9417004 Datta这里提出的研究解决了三个不同领域的基本问题：a）强调参数不确定性的鲁棒控制，B）强调鲁棒性和性能问题的自适应控制，以及c）鲁棒自适应控制与推力正在发展新的定量分析和设计方法，利用最近爆炸的结果，Kharitonov定理及其扩展 首先，我们打算开发“最佳情况”的结果，涉及参数的稳定裕度，胡稳定裕度（范数），增益和相位裕度的参数化的传递函数，如区间植物。 这些鲁棒性结果在鲁棒参数稳定性领域，然后将被用于非保守地量化自适应控制方案的鲁棒性。 第二个目标是发展极值参数的结果，涉及H2和L1规范，我们相信，将发挥重要作用，在研究自适应系统的性能。 第三个目标是解决自适应控制和鲁棒参数稳定性领域中的一些重要的公开问题。 上述目标的动机，从我们以前的研究，这不仅使我们能够确定一些突出的未解决的问题，在自适应控制和鲁棒参数稳定性的领域，但也强调了需要在这两个传统的非常不同的领域的跨学科的研究工作。 这两个领域中的任何一个现有理论都不能以实际或令人满意的方式解决与这一建议有关的问题。 然而，从理论和实践的角度来看，必须成功地解决这些问题。 实际上，鲁棒控制和自适应控制的实践者从我们寻求发展的"非保守"参数L1和Hoo鲁棒性结果中受益匪浅。 ***

August 2, 19959417004 Datta The research proposed here addresses fundamental problems in three distinct areas: a)Robust Control with an emphasis on parametric uncertainty b)Adaptive Control with an emphasis on robustness and performance issues and c)Robust Adaptive Control with the thrust being the development of new quantitative analysis and design methods exploiting the recent explosion of results obtained using Kharitonov's Theorem and its extensions. First, we intend to develop "best case" results involving the parametric stability margin, Hoo stability margin (norm), gain and phase margins over a parametrized set of transfer functions, such as an interval plant. These robustness results in the area of Robust Parametric Stability, would then be used for non- conservatively quantifying the robustness of adaptive control schemes. The second objective is to develop extremal parametric results involving the H2 and L1 norms which, we believe, will play an important role in studying adaptive system performance. The third objective is to address some important open problems in each of the areas of adaptive control and robust parametric stability. The objectives mentioned above are motivated from our prior research which has not only enabled us to identify some of the outstanding unresolved problems in the areas of adaptive control and robust parametric stability, but has also highlighted the need for inter-twined research efforts in these two traditionally very diverse fields. None of the existing theory in either of these fields can solve the problems related to this proposal in a practical or satisfactory manner. However, successful resolution of these problems is imperative from both a theoretical and a practical point of view. Indeed, practitioners of both robust and adaptive control stand to benefit a lot from the "non- conservative" parametric L1 and Hoo robustness results that we seek to develop. ***