Aircraft Runway Acceleration in the Presence of Severe Wind Gusts

  • Nikolai BotkinEmail author
  • Varvara Turova
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 494)


This paper concerns the problem of aircraft control during the takeoff roll in the presence of severe wind gusts. It is assumed that the aircraft moves on the runway with a constant axial acceleration from a stationary position up to a specific speed at which the aircraft can go into flight. The lateral motion is controlled by the steering wheel and the rudder and affected by side wind. The aim of control is to prevent rolling out of the aircraft from the runway strip. Additionally, the lateral deviation, lateral speed, yaw angle, and yaw rate should remain in certain thresholds during the whole takeoff roll. The problem is stated as a differential game with state constraints. A grid method for computing the value function and optimal feedback strategies for the control and disturbance is used. The paper deals both with a nonlinear and linearized models of an aircraft on the ground. Simulations of the trajectories are presented.


Aircraft runway Lateral runway model Differential game Grid method 



This work is supported by the DFG grant TU427/2-1.


  1. 1.
    Barnes, A.G., Yager, T.J.: Enhancement of aircraft ground handling simulation capability. Technical report AGARDograph 333. AGARD (1998)Google Scholar
  2. 2.
    Rankin, J.: Bifurcation analysis of nonlinear ground handling of aircraft. Dissertation, University of Bristol (2010)Google Scholar
  3. 3.
    Klyde, D.H., Myers, T.T., Magdaleno, R.E., Reinsberg, J.G.: Identification of the dominant ground handling characteristics of a navy jet trainer. J. Guid. Control Dyn. 25(3), 546–552 (2002)CrossRefGoogle Scholar
  4. 4.
    Duprez, J., Mora-Camino, F., Villaume, F.: Control of the aircraft-on-ground lateral motion during low speed roll and manoeuvers. In: Proceedings of the 2004 IEEE Aerospace Conference, vol. 4, pp. 2656–2666 (2004)Google Scholar
  5. 5.
    Roos, C., Biannic, J.M.: Aircraft-on-ground lateral control by an adaptive LFT-based anti-windup approach. In: 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control, pp. 2207–2212 (2006)Google Scholar
  6. 6.
    De Hart, R.D.: Advanced take-off and flight control algorithms for fixed wing unmanned aerial vehicles. Masters Dissertation, University of Stellenbosch (2010)Google Scholar
  7. 7.
    Essuri, M., Alkurmaji, K., Ghmmam, A.: Developing a dynamic model for unmanned aerial vehicle motion on ground during takeoff phase. Appl. Mech. Mater. 232, 561–567 (2012)CrossRefGoogle Scholar
  8. 8.
    Botkin, N.D., Krasov, A.I.: Positional control in a model problem of aircraft take-off while on the runway. In: Subbotin, A.I., Tarasiev, A.M. (eds.) Positional Control with Guaranteed Result, vol. 113, pp. 22–32. Akad Nauk SSSR, Ural. Otdel., Inst. Matem. i Mekhan., Sverdlovsk (1988). (in Russian)Google Scholar
  9. 9.
    Krasovskii, N.N., Subbotin, A.I.: Game-Theoretical Control Problems. Springer, New York (1988)CrossRefGoogle Scholar
  10. 10.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    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.) ICNAAM-2012. AIP Conference Proceedings, vol. 1479, pp. 1226–1229. The American Institute of Physics, Melville (2012)Google Scholar
  13. 13.
    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. Birkäuser, Boston (2013)CrossRefGoogle Scholar
  14. 14.
    Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277, 1–47 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Subbotin, A.I.: Generalized Solutions of First Order PDEs: The Dynamical Optimization Perspective. Birkhäuser, Boston (1995)CrossRefzbMATHGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  1. 1. Zentrum MathematikTechnische Universität MünchenGarching bei MünchenGermany

Personalised recommendations