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

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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. ***