Journal of Optimization Theory and Applications

, Volume 83, Issue 2, pp 237–267 | Cite as

Control of an aircraft landing in windshear

  • V. S. Patsko
  • N. D. Botkin
  • V. M. Kein
  • V. L. Turova
  • M. A. Zarkh
Contributed Papers


The problem of the feedback control of an aircraft landing in the presence of windshear is considered. The landing process is investigated up to the time when the runway threshold is reached. It is assumed that the bounds on the wind velocity deviations from some nominal values are known, while information about the windshear location and wind velocity distribution in the windshear zone is absent. The methods of differential game theory are employed for the control synthesis.

The complete system of aircraft dynamic equations is linearized with respect to the nominal motion. The resulting linear system is decomposed into subsystems describing the vertical (longitudinal) motion and lateral motion. For each subsystem, an, auxiliary antagonistic differential game with fixed terminal time and convex payoff function depending on two components of the state vector is formulated. For the longitudinal motion, these components are the vertical deviation of the aircraft from the glide path and its time derivative; for the lateral motion, these components are the lateral deviation and its time derivative. The first player (pilot) chooses the control variables so as to minimize the payoff function; the interest of the second player (nature) in choosing the wind disturbance is just opposite.

The linear differential games are solved on a digital computer with the help of corresponding numerical methods. In particular, the optimal (minimax) strategy is obtained for the first player. The optimal control is specified by means of switch surfaces having a simple structure. The minimax control designed via the auxiliary differential game problems is employed in connection with the complete nonlinear system of dynamical equations.

The aircraft flight through the wind downburst zone is simulated, and three different downburst models are used. The aircraft trajectories obtained via the minimax control are essentially better than those obtained by traditional autopilot methods.

Key Words

Flight mechanics landing feedback control windshear problems differential games longitudinal motion lateral motion numerical methods linear differential games switch surfaces 



mean aerodynamic chord, m


aerodynamic force coefficients, body-axes system


acceleration of gravity, m sec−2


inertia moments, kg m2


wing span, m


aircraft mass, kg


aerodynamic moment coefficients, body-axes system


aerodynamic moments, N m


thrust force, N


dynamic pressure, kg m−1 sec−2


reference surface, m2


absolute velocity, m sec−1

\(\hat V\)

relative velocity, m sec−1


wind velocity, m sec−1


absolute velocity components, m sec−1

\(\hat V_{xg} ,\hat V_{yg} ,\hat V_{zg} \)

relative velocity components, m sec−1


wind velocity components, m sec−1


coordinates of the aircraft center of mass, m, ground-fixed system


angle of attack, deg


sideslip angle, deg


bank angle, deg


aileron deflection, deg


elevator deflection, deg


rudder deflection, deg


aileron setting (control), deg


elevator setting (control), deg


engine control lever setting, deg


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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • V. S. Patsko
    • 1
  • N. D. Botkin
    • 1
  • V. M. Kein
    • 2
  • V. L. Turova
    • 1
  • M. A. Zarkh
    • 1
  1. 1.Institute of Mathematics and MechanicsRussian Academy of SciencesEkaterinburgRussia
  2. 2.Civil Afviration AcademySt. PetersburgRussia

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