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Homotopy Methods in Control System Design and Analysis

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Advances in Optimization and Numerical Analysis

Part of the book series: Mathematics and Its Applications ((MAIA,volume 275))

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Abstract

Recent technologies have led to stringent control system requirements. This has increased the importance and complexity of the analysis and design of control systems, which often require the solution of systems of nonlinear equations of high order. Some challenging computational problems in control design include model order reduction, high dimensional Riccati equations, fixed-structure optimization, robust analysis and feedback synthesis, sensor/actuator placement, and simultaneous controller/structure design. This paper describes these problems, and the directions in which globally convergent homotopy methods must be extented in order to be applicable to computational problems in control. By way of illustration, a computationally effective probability-one homotopy algorithm is presented for the optimal projection formulation of the reduced order model problem, together with some numerical results.

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Authors and Affiliations

  1. Department of Computer Science, Virginia Polytechnic Institute & State University, Blacksburg, VA, 24061-0106, USA

    Layne T. Watson

  2. Government Aerospace Systems Division, Harris Corporation, MS 22-4848, Melbourne, FL, 32902, USA

    Stephen Richter

  3. Department of Computer Science, Virginia Polytechnic Institute & State University, Blacksburg, VA, 24061-0106, USA

    Dragan Žigić

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  1. Layne T. Watson
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  2. Stephen Richter
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  1. Instituto de Investigaciones en Mátematicas Aplicadas y Sistemas, Universidad Nacional Autónoma de México, México

    Susana Gomez  & Jean-Pierre Hennart  & 

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Watson, L.T., Richter, S., Žigić, D. (1994). Homotopy Methods in Control System Design and Analysis. In: Gomez, S., Hennart, JP. (eds) Advances in Optimization and Numerical Analysis. Mathematics and Its Applications, vol 275. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8330-5_8

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  • DOI: https://doi.org/10.1007/978-94-015-8330-5_8

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