Skip to main content

Dynamic Programming Approach to Aircraft Control in a Windshear

  • Chapter
  • First Online:

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 13))

Abstract

Application of a dynamic programming method to the problem of aircraft control during take-off in a windshear is considered. A simplified four-dimensional model of the aircraft dynamics is used, and stable numerical algorithms for solving Hamilton–Jacobi–Bellman–Isaacs equations arising from differential games with state constraints are utilized for the design of feedback controls.

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

Buying options

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

Learn about institutional subscriptions

References

  • Botkin N, Kein V, Patsko V, Turova V, Zarkh M (1993) Differential games and aircraft control problems in the presence of wind disturbances. Izv Ross Akad Nauk, Tekhn Kibernet 1:68–76, translated as J Comput Syst Sci Int 32(3):110–117 (1994)

    Google Scholar 

  • Botkin N, Hoffmann KH, Mayer N, Turova V (2011a) Approximation schemes for solving disturbed control problems with non-terminal time and state constraints. Analysis 31:355–379

    Article  MathSciNet  MATH  Google Scholar 

  • Botkin N, Hoffmann KH, Turova V (2011b) Stable numerical schemes for solving Hamilton–Jacobi–Bellman–Isaacs equations. SIAM J Sci Comp 33(2):992–1007

    Article  MathSciNet  MATH  Google Scholar 

  • Chen Y, Pandey S (1989) Robust control strategy for take-off performance in a windshear. Optim Control Appl Methods 10(1):65–79

    Article  MathSciNet  MATH  Google Scholar 

  • Krasovskii N, Subbotin A (1974) Positional differential games. Nauka, Moscow, in Russian

    MATH  Google Scholar 

  • Krasovskii N, Subbotin A (1988) Game-theoretical control problems. Springer, New York

    Book  MATH  Google Scholar 

  • Leitmann G, Pandey S (1990) Aircraft control under conditions of windshear. In: Leondes C (ed) Control and dynamic systems, vol 34. Academic Press, New York, pp 1–79

    Google Scholar 

  • Leitmann G, Pandey S (1991) Aircraft control for flight in an uncertain environment: Takeoff in windshear. J Optim Theory Appl 70(1):25–55

    Article  MathSciNet  MATH  Google Scholar 

  • Leitmann G, Pandey S, Ryan E (1993) Adaptive control of aircraft in windshear. Int J Robust Nonlinear Control 3:133–153

    Article  MATH  Google Scholar 

  • Miele A, Wang T, Melvin W (1986a) Guidance strategies for near-optimum take-off performance in a windshear. J Optim Theory Appl 50(1):1–47

    Article  MathSciNet  MATH  Google Scholar 

  • Miele A, Wang T, Melvin W (1986b) Optimal take-off trajectories in the presence of windshear. J Optim Theory Appl 49(1):1–45

    Article  MathSciNet  MATH  Google Scholar 

  • Mößner B, Reif U (2009) Error bounds for polynomial tensor product interpolation. Computing 86(2–3):185–197

    Article  MathSciNet  MATH  Google Scholar 

  • Subbotin A (1995) Generalized solutions of first order PDEs: The dynamical optimization perspective. Birkhäuser, Boston

    Google Scholar 

  • Subbotin A, Chentsov A (1981) Optimization of guaranteed result in control problems. Nauka, Moscow, in Russian

    Google Scholar 

  • Turova V (1991) Take-off control in a windshear. Tech. Rep., Preprint of the Inst Math Mech, Ekaterinburg

    Google Scholar 

Download references

Acknowledgments

The authors are grateful to anonymous reviewer for his constructive and helpful comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nikolai D. Botkin .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Botkin, N.D., Turova, V.L. (2013). Dynamic Programming Approach to Aircraft Control in a Windshear. In: Křivan, V., Zaccour, G. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 13. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-02690-9_3

Download citation

Publish with us

Policies and ethics