Optimal Abort Landing in the Presence of Severe Windshears

Conference paper
First Online:
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 494)

Abstract

In this paper, the abort landing problem is considered with reference to a point-mass aircraft model describing flight in a vertical plane. It is assumed that the pilot linearly increases the power setting to maximum upon sensing the presence of a windshear. This option is accounted for in the aircraft model and is not considered as a control. The only control is the angle of attack, which is assumed to lie between minimum and maximum values. The aim of this paper is to construct a feedback strategy that ensures a safe abort landing. An algorithm for solving nonlinear differential games is used for the design of such a strategy. The feedback strategy obtained is discontinuous in time and space so that realizations of control may have a bang-bang structure. To be realistic, outputs of the feedback strategy are being smoothed in time, and this signal is used as control.

Keywords

Aircraft model Penetration landing Abort landing Differential game Hamilton-Jacobi equation Grid method Feedback strategy Optimal trajectories 
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Notes

Acknowledgements

This work was supported in part by the DFG grant TU427/2-1.

References

  1. 1.
    Miele, A., Wang, T., Melvin, W.W.: Optimal take-off trajectories in the presence of windshear. J. Optim. Theory Appl. 49, 1–45 (1986)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Miele, A., Wang, T., Melvin, W.W.: Guidance strategies for near-optimum take-off performance in windshear. J. Optim. Theory Appl. 50(1), 1–47 (1986)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Chen, Y.H., Pandey, S.: Robust control strategy for take-off performance in a windshear. Optim. Control Appl. Methods 10(1), 65–79 (1989)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Leitmann, G., Pandey, S.: Aircraft control under conditions of windshear. In: Leondes, C.T. (ed.) Control and Dynamic Systems, Part 1, vol. 34, pp. 1–79. Academic Press, New York (1990)Google Scholar
  5. 5.
    Leitmann, G., Pandey, S.: Aircraft control for flight in an uncertain environment: takeoff in windshear. J. Optim. Theory Appl. 70(1), 25–55 (1991)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Leitmann, G., Pandey, S., Ryan, E.: Adaptive control of aircraft in windshear. Int. J. Robust Nonlinear 3, 133–153 (1993)CrossRefMATHGoogle Scholar
  7. 7.
    Botkin, N.D., Turova, V.L.: Application of dynamic programming approach to aircraft take-off in a windshear. In: Simos, T.E., Psihoyios, G., Tsitouras, C., Zacharias, A. (eds.) AIP Conference Proceedings, ICNAAM-2012, vol. 1479, pp. 1226–1229. AIP, Melville (2012)Google Scholar
  8. 8.
    Botkin, N.D., Turova, V.L.: Dynamic programming approach to aircraft control in a windshear. In: Křivan, V., Zaccour, G. (eds.) Advances in Dynamic Games: Theory, Applications, and Numerical Methods. Annals of the International Society of Dynamic Games, vol. 13, pp. 53–69 (2013)Google Scholar
  9. 9.
    Krasovskii, N.N., Subbotin, A.I.: Game-Theoretical Control Problems. Springer, New York (1988)CrossRefGoogle Scholar
  10. 10.
    Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277, 1–47 (1983)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Subbotin, A.I.: Generalized Solutions of First Order PDEs: The Dynamical Optimization Perspective. Birkhäuser, Boston (1995)CrossRefMATHGoogle Scholar
  12. 12.
    Botkin, N.D., Hoffmann, K.-H., Mayer, N., Turova, V.L.: Approximation schemes for solving disturbed control problems with non-terminal time and state constraints. Analysis 31, 355–379 (2011)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Botkin, N.D., Hoffmann, K.-H., Turova, V.L.: Stable numerical schemes for solving Hamilton-Jacobi-Bellman-Isaacs equations. SIAM J. Sci. Comput. 33(2), 992–1007 (2011)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Patsko, V.S., Botkin, N.D., Kein, V.M., Turova, V.L., Zarkh, M.A.: Control of an aircraft landing in windshear. J. Optim. Theory Appl. 83(2), 237–267 (1994)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Miele, A., Wang, T., Wang, H., Melvin, W.W.: Optimal penetration landing trajectories in the presence of windshear. J. Optim. Theory Appl. 57(1), 1–40 (1988)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Miele, A., Wang, T., Tzeng, C.Y., Melvin, W.W.: Optimal abort landing trajectories in the presence of windshear. J. Optim. Theory Appl. 55(2), 165–202 (1987)CrossRefMATHGoogle Scholar
  17. 17.
    Bulirsch, R., Montrone, F., Pesch, H.J.: Abort landing in the presence of a windshear as a minimax optimal control problem, part 1: necessary conditions. J. Optim. Theory Appl. 70(1), 1–23 (1991)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Bulirsch, R., Montrone, F., Pesch, H.J.: Abort landing in the presence of a windshear as a minimax optimal control problem, part 2: multiple shooting and homotopy. J. Optim. Theory Appl. 70(2), 223–254 (1991)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Berkmann, P., Pesch, H.J.: Abort landing in windshear: optimal control problem with third-order state constraint and varied switching structure. J. Optim. Theory Appl. 85(1), 21–57 (1995)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Turova, V.L.: Application of numerical methods of the theory of differential games to the problems of take-off and abort landing. In: Osipov, Y. (ed.) Proceedings of the Institute of Mathematics and Mechanics, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg, vol. 2., pp. 188–201 (1992). (in Russian)Google Scholar
  21. 21.
    Pflüger, D.: Spatially adaptive sparse grids for higher-dimensional problems. Dissertation, Verlag Dr. Hut, München (2010)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  1. 1.Zentrum MathematikTechnische Universität MünchenGarching bei MünchenGermany

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