Advances in Robust Control; and in High Resolution Spectral Estimation

本文提出的研究代表了我们目前的计划，在开发理论和计算工具的建模和控制的动力系统的延续。 我们的计划是研究两个主要课题。1.非线性系统的鲁棒控制。我们的方法依赖于图的概念。 模型的不确定性量化使用适当的推广的差距度量，衡量潜在的图形扰动。 鲁棒控制理论与鲁棒裕度的显式表达式到位。 此外，在我们最近的工作中已经提出了一种计算方法。 建议的研究重点是如何（i）提高计算工具的有效性，以及寻求更有效的，（ii）扩展基本的鲁棒性理论的基本范式以外的平衡或预先指定的轨迹稳定。 特别是，我们要评估的振荡系统的鲁棒性，以及系统中存在的不确定性偏差。高分辨率谱估计。这一方向的推动力是由最近与克里斯·伯恩斯和安德斯·林奎斯特的联合工作提供的。 我们已经介绍了滤波器组，并随后一般的输入状态（IS）滤波器，用于提供选定的频谱间隔的谐波放大。 我们正在完成一个一般的理论，利用这种过滤器的选择性，并允许非常高的分辨率谱估计的过程中。 特别是，对于识别噪声中的正弦曲线，这是雷达和声纳应用中的一个关键问题，我们的方法已经允许显着更好的分辨率比标准的最先进的MUSIC和ESPRIT算法。

The research proposed herein represents a continuation of our current program in developing theoretical and computational tools for modeling and control of dynamical systems. Our plan is to investigate two main topics. 1. Robust control of nonlinear systems.Our approach relies on the concept of the graph. Model uncertainty is quantified using a suitable generalization of the gap metric which measures potential graph perturbations. A theory of robust control with explicit expressions for robustness margin is in place. Also, a computational approach has been presented in our recent work. The proposed research focuses on how to (i) enhance the effectiveness of the computational tools as well as seek more effective ones, (ii) extend the basic robustness theory outside the basic paradigm of stability about an equilibrium or a prespecified trajectory. In particular, we want to assess robustness of oscillatory systems, and systems in the presence of uncertain biases.2. High-resolution spectral estimation.The impetus for this direction was provided by recent joint work with Chris Byrnes and Anders Linquist. We have introduced filter banks, and subsequently general input-to-state (IS) filters, for providing harmonic amplification of selected spectral intervals. We are in the process of completing a general theory which takes advantage of the selectivity properties of such filters and allows very high resolution spectral estimation. In particular, for identifying sinusoids in noise, which is a key problem in radar and sonar applications, our approach has already permitted significantly better resolution than standard state-of-the-art MUSIC and ESPRIT algorithms.