Career: A Career Development Plan in Optimal and Robust Control Theory and Application

小行星9624152 在这个建议中概述的研究工作是统一的发展现有的范例在各种新的问题，其中一些接触到其他领域，如非线性系统的灵敏度和识别的鲁棒性和最优控制的想法。 我们研究的出发点是鲁棒数字控制问题。 我们认为，一个数字控制系统是一个连续时间和离散时间系统的混合物，所产生的周期性行为，以及相关的非线性量化效应，由于有限字长计算。 对于这个问题的问题是开发一个系统的理论，可以分析性能之间的权衡采样率，周期性行为，和量化效果。 这样的理论目前还不存在。 这导致我们在两个不同的方向开发兼容的技术，具有广泛的适用性。 首先，我们开发了一个框架的分析和综合的混合连续时间离散时间系统，扩展了主要研究者以前的工作采样数据鲁棒控制。 第二个方向涉及分析系统的开关非线性，如继电器，滞后，量化。 我们表明，通过多速率采样技术（类似于信号处理中的Σ-Δ调制器），开关非线性的许多问题相当于分析一个LTI系统的反馈与继电器。 我们解决的问题，计算极限环和它们的灵敏度的输入输出loo非线性的这类系统。这一努力似乎提供了鲁棒控制和某些类型的所谓的“智能系统”之间的联系。" 在一个平行的和相关的努力，L1模型简化问题的解决和它的意义作为一个“好”的规范模型简化概述。 从大系统降阶鲁棒控制器设计的角度也提出了这一问题。 在面向控制的识别领域，我们解决了新的问题的参数变化系统的识别，其模型将是更有用的过程控制问题，如在半导体制造的实时控制，和情况下，底层的过程进行快速变化的操作条件，其中一个单一的LTI模型是不合适的。 初步结果概述，以及它们的连接和意义的识别和建模的basteroural框架。 该职业计划的教育部分是由控制和系统理论基本上是跨学科的原则指导的。 这种想法在跨部门边界的研究问题中很明显。 在教育方面，这可以通过跨部门课程和实验室进行。 首席调查员目前参与建立一个部门间控制实验室，这将指导建立控制和系统方面的共同课程。 该计划的另一个组成部分是将最近的研究成果纳入更新研究生和本科生课程。 具体而言，我们概述了正在进行的努力，将最近的结果采样数据控制从混合动力系统的角度来看，在数字控制课程。 ***

9624152 Bamieh The research efforts outlined in this proposal are unified by the idea of developing the existing paradigms in robust and optimal control in a variety of novel problems, some of which make contact with other areas such as nonlinear systems sensitivity and identification. The starting point of our investigations is the problem of robust digital control. We take the view that a digital control system is a mixture of continuous-time and discrete-time systems, with the resulting periodic behaviour, and the related nonlinear quantization effects due to finite wordlength computations. For this problem the issue is to develop a systematic theory where one can analyze performance tradeoffs between sampling rates, periodic behaviour, and quantization effects. Such a theory does not at present exist. This leads us to develop compatible techniques in two different directions with a wide range of applicability. First, we develop a framework for the analysis and synthesis of mixed continuous-time discrete-time systems which extends the principal investigators previous work on sampled-data robust control. The second direction involves the analysis of systems with switching nonlinearities such as relays, hysterisis, and quantization. We show via a multirate sampling technique (akin to Sigma-Delta modulators in signal processing) that many problems with switching nonlinearities are equivalent to analyzing a LTI system in feedback with a relay. We address the problems of computing limit cycles and their sensitivities in terms of the input-output loo nonlinear for such systems. This effort seems to provide a connection between robust control and certain types of so-called "intelligent systems." In a parallel and related effort, the L1 model reduction problem is addressed and its significance as a "good" norm for model reduction is outlined. This problem is also motivated from the perspective of reduced order robust controller design for la rge scale systems. In the area of control oriented identification, we address the novel problem of the identification of parameter varying systems, whose models would be more useful for process control problems such as in the real-time control of semiconductor manufacturing, and situations where the underlying processes undergo rapid changes in operating conditions, for which a single LTI model is inappropriate. Preliminary results are outlined as well as their connection and implication for identification and modeling in the bahavioural framework. The educational part of this career plan is guided by the principle that control and systems theory are fundamentally interdisciplinary subjects. This idea is apparent in research problems that cross departmental boundaries. In education, this can be carried out with interdepartmental courses and laboratories. The current involvement of the principal investigator in the establishment of an interdepartmental controls laboratory, will be a guide to the establishment of common courses in controls and systems. Another component in this plan is the incorporation of recent research results to update graduate and undergraduate courses. Specifically, we outline ongoing efforts at incorporating recent results on sampled-data control from the hybrid systems point of view in digital control courses. ***