Skip to main content
SpringerLink
Log in

Applied Algebraic Geometry in Model Based Design for Manufacturing

  • Conference paper
  • First Online:
The Impact of Applications on Mathematics

Part of the book series: Mathematics for Industry ((MFI,volume 1))

  • 948 Accesses

Abstract

In this paper we show the interplay of real algebraic geometry and control system design in manufacturing from the standpoint “how applications affect to algorithm development in real algebraic geometry”. One of important perspectives of the interaction is how we overcome the inherent computational complexity for solving practical problems and the key point is making good use of their special structures of the practical problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Akahori, I., Hara, S.: Computer aided control system analysis and design based on the concept object-orientation (in Japanese). Trans. SICE 24(5), 506–513 (1988)

    Google Scholar 

  2. Anai, H., Hara, S.: Fixed-structure robust controller synthesis based on sign definite condition by a special quantifier elimination. In: Proceedings of American Control Conference, pp. 1312–1316 (2000)

    Google Scholar 

  3. Anai, H., Hara, S.: A parameter space approach to fixed-order robust controller synthesis by quantifier elimination. Int. J. Control 79(11), 1321–1330 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. Caviness, B.F., Johnson, J.R. (eds.): Quantifier Elimination and Cylindrical Algebraic Decomposition. Springer, New York (1998)

    MATH  Google Scholar 

  5. Collins, G.E.: Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition, LNCS 32. Springer, Berlin (1975)

    Google Scholar 

  6. Collins, G.E., Hong, H.: Partial cylindrical algebraic decomposition for quantifier elimination. J. Symbolic Comput. 12(3), 299–328 (Sept. 1991)

    Google Scholar 

  7. Didier, H., Andrea, G. : Positive Polynomials in Control. Lecture Notes in Control and Information Sciences, vol. 312. Springer, Berlin (2005)

    Google Scholar 

  8. Dolzmann, A., Sturm, T.: Redlog: computer algebra meets computer logic. ACM SIGSAM Bull. 31(2), 2–9 (1997)

    Article  MathSciNet  Google Scholar 

  9. Dorato, P., Yang, W., Abdallah, C.: Robust multi-objective feedback design by quantifier elimination. J. Symb. Comp. 24, 153–159 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. González-Vega, L.: A combinatorial algorithm solving some quantifier elimination problems. In: Caviness, B., Johnson, J. (eds.) Quantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation, pp. 365–375. Springer, Berlin (1998)

    Google Scholar 

  11. Hyodo, N., Hong, M., Yanami, H., Hara, S., Anai, H.: Solving and visualizing nonlinear parametric constraints in control based on quantifier elimination. Appl. Algebra Eng. Commun. Comput. 18(6), 497–512 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Iwane, H., Higuchi, H., Anai, H.: (2013) An effective implementation of a special quantifier elimination for a sign definite condition by logical formula simplification. In: ASC 2013: Lecture Notes in Computer Science, vol. 8136, pp. 194–208. Springer, Berlin (2013)

    Google Scholar 

  13. Iwane, H., Yanami, H., Anai, H.: A symbolic-numeric approach to multi-objective optimization in manufacturing design. Math. Comput. Sci. 5(3), 315–334 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  14. Iwane, H., Yanami, H., Anai, H., Yokoyama, K.: An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination. Theor. Comput. Sci. 479, 43–69 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  15. Jirstrand, M.: Nonlinear control system design by quantifier elimination. J. Symb. Comp. 24(2), 137–152 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Loos, R., Weispfenning, V.: Applying linear quantifier elimination. Comput. J. 36(5), 450–462 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  17. Matsui, Y., Iwane, H., Anai, H.: Development of Computer Algebra Research and Collaboration with Industry, MI Lecture Note Series, vol 49, pp. 43–52. Kyushu University (2013)

    Google Scholar 

  18. Saito, O.: Computer aided control engineering: periphery of control engineering and computer algebraic manipulation (in Japanese). Syst. Control 29(12), 785–794 (1985)

    Google Scholar 

  19. Seidenberg, A.: A new decision method for elementary algebra. Ann. Math. 60, 365–374 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  20. Strzeboński, A.W.: Cylindrical algebraic decomposition using validated numerics. J. Symbolic Comput. 41(9), 1021–1038 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  21. Sturm, T.: New domains for applied quantifier elimination. In: Proceedings of the 14th International Workshop on Computer Algebra (CASC) 2006, pp. 295–301 (2006)

    Google Scholar 

  22. Tarski, A.: Decision Methods for Elementary Algebra and Geometry. University of California Press, Berkeley (1951)

    Google Scholar 

  23. Weispfenning, V.: The complexity of linear problems in fields. J. Symbolic Comput. 5(1–2), 3–27 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  24. Weispfenning, V.: Simulation and optimization by quantifier elimination. J. Symb. Comput. 24(2), 189–208 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  25. Weispfenning, V.: A new approach to quantifier elimination for real algebra. In: Caviness, F., Johnson, J.R. (eds.) Quantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation, pp. 376–392. Springer, Berlin (1998)

    Google Scholar 

  26. Yoshimura, S., Iki, H., Uriu, Y., Anai, H., Hyodo, N.: Generator excitation control using a parameter space design method. In: 43rd International Universities Power Engineering Conference (UPEC 2008), pp. 1–4 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Knowledge Platforms Laboratories, Fujitsu Laboratories Ltd., 4-1-1 Kamikodanaka, Nakaharaku, Kawasaki, Kanagawa, 211-8588, Japan

    Hirokazu Anai

  2. Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Hirokazu Anai

Authors
  1. Hirokazu Anai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hirokazu Anai .

Editor information

Editors and Affiliations

  1. Institute for Mathematics and Industry, Kyushu University, Fukuoka, Japan

    Masato Wakayama

  2. CSIRO (Commonwealth Scientific and Industrial Research Organisation), Canberra, Aust Capital Terr, Australia

    Robert S. Anderssen

  3. School of Mathematical Sciences, Fudan University, Shanghai, China

    Jin Cheng

  4. Kyushu University, Fukuoka, Japan

    Yasuhide Fukumoto

  5. Institute of Natural and Mathematical Sciences, Massey University, Palmerston North, Auckland, New Zealand

    Robert McKibbin

  6. Institute of Mathematics, Free University of Berlin, Berlin, Germany

    Konrad Polthier

  7. Kyushu University, Fukuoka, Japan

    Tsuyoshi Takagi

  8. Department of Mathematics, National University of Singapore, Singapore, Singapur, Singapore

    Kim-Chuan Toh

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Japan

About this paper

Cite this paper

Anai, H. (2014). Applied Algebraic Geometry in Model Based Design for Manufacturing. In: Wakayama, M., et al. The Impact of Applications on Mathematics. Mathematics for Industry, vol 1. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54907-9_13

Download citation

  • DOI: https://doi.org/10.1007/978-4-431-54907-9_13

  • Published:

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-54906-2

  • Online ISBN: 978-4-431-54907-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation