Robust Adaptive Control Based on Kharitonov Theory and Its Extensions

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；c)鲁棒自适应控制的推力是开发新的定量分析和设计方法，利用最近使用Kharitonov定理及其扩展获得的大量结果。首先，我们打算开发“最佳情况”结果，涉及参数稳定裕度，Hoo稳定裕度（范数），增益和相位裕度在参数化传递函数集上，如区间工厂。这些鲁棒性结果在鲁棒参数稳定性领域，然后将用于非保守量化自适应控制方案的鲁棒性。第二个目标是开发涉及H2和L1范数的极值参数结果，我们相信这将在研究自适应系统性能中发挥重要作用。第三个目标是在自适应控制和鲁棒参数稳定性的各个领域解决一些重要的开放问题。上述目标的动机来自于我们之前的研究，这不仅使我们能够确定自适应控制和鲁棒参数稳定性领域的一些悬而未决的问题，而且还强调了在这两个传统上非常多样化的领域进行相互交织的研究工作的必要性。这两个领域的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，成功地解决这些问题是势在必行的。事实上，鲁棒控制和自适应控制的实践者都从我们寻求发展的“非保守”参数L1和Hoo鲁棒性结果中获益良多。＊＊＊

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. ***