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Switching surfaces and groebner bases

  • Part A Learning And Computational Issues
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Learning, control and hybrid systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 241))

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Abstract

A number of problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control. Recently, a powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested, namely the use of Groebner bases. In this note, we apply the Groebner basis technique to find effective solutions to the classical problem of time-optimal control.

This work was supported in part by grants from the National Science Foundation ECS-99700588, ECS-9505995, NSF-LIS, by the Air Force Office of Scientific Research AF/F49620-94-1-0461, AF/F49620-98-1-0168, by the Army Research Office DAAH04-94-G-0054, DAAG55-98-1-0169, and MURI Grant.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Minnesota, 55455, Minneapolis, MN

    Allen Tannenbaum

Authors
  1. Tryphon Georgiou
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  2. Allen Tannenbaum
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Editor information

Yutaka Yamamoto PhD Shinji Hara PhD

Additional information

This paper is dedicated with warm friendship to Bruce Francis and M. Vidyasagar on the occasion of their 50th birthday.

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© 1999 Springer-Verlag London Limited

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Georgiou, T., Tannenbaum, A. (1999). Switching surfaces and groebner bases. In: Yamamoto, Y., Hara, S. (eds) Learning, control and hybrid systems. Lecture Notes in Control and Information Sciences, vol 241. Springer, London. https://doi.org/10.1007/BFb0109722

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  • DOI: https://doi.org/10.1007/BFb0109722

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-076-7

  • Online ISBN: 978-1-84628-533-2

  • eBook Packages: Springer Book Archive

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