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

本提案中概述的研究工作是由在各种新问题中发展鲁棒和最优控制的现有范例的想法统一的，其中一些涉及其他领域，如非线性系统的灵敏度和识别。我们研究的起点是鲁棒数字控制问题。我们认为数字控制系统是连续时间和离散时间系统的混合，具有由此产生的周期性行为，以及由于有限字长计算而产生的相关非线性量化效应。对于这个问题，问题是要发展一个系统的理论，在这个理论中，人们可以分析采样率、周期行为和量化效果之间的性能权衡。这样的理论目前还不存在。这导致我们在两个不同的方向上开发具有广泛适用性的兼容技术。首先，我们开发了一个用于分析和综合混合连续-离散系统的框架，它扩展了主要研究人员以前在采样数据鲁棒控制方面的工作。第二个方向涉及对具有开关非线性的系统的分析，如继电器、迟滞和量化。我们通过多速率采样技术（类似于信号处理中的Sigma-Delta调制器）表明，许多与开关非线性有关的问题相当于分析带有继电器的反馈LTI系统。我们针对这类系统的输入输出非线性，讨论极限环及其灵敏度的计算问题。这种努力似乎提供了鲁棒控制和某些类型的所谓“智能系统”之间的联系。在一个平行的和相关的工作中，L1模型简化问题被处理，并且它作为模型简化的“好”规范的重要性被概述。从大系统的降阶鲁棒控制器设计的角度出发，对该问题进行了研究。在面向控制的识别领域，我们解决了参数变化系统识别的新问题，其模型对于过程控制问题更有用，例如半导体制造的实时控制，以及底层过程在操作条件下经历快速变化的情况，单个LTI模型是不合适的。初步结果概述，以及他们的联系和含义识别和建模的行为框架。这个职业规划的教育部分以控制和系统理论基本上是跨学科学科的原则为指导。这个想法在跨部门的研究问题中很明显。在教育方面，这可以通过跨部门的课程和实验室来实现。目前主要研究人员参与建立一个部门间控制实验室，这将是建立控制和系统共同课程的指南。该计划的另一个组成部分是将最新的研究成果纳入研究生和本科课程。具体而言，我们概述了正在进行的努力，从混合系统的角度将采样数据控制的最新结果纳入数字控制课程。＊＊＊

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. ***