Abort landing in windshear: Optimal control problem with third-order state constraint and varied switching structure View Full Text


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Article Info

DATE

1995-04

AUTHORS

P. Berkmann, H. J. Pesch

ABSTRACT

Optimal abort landing trajectories of an aircraft under different windshear-downburst situations are computed and discussed. In order to avoid an airplane crash due to severe winds encountered by the aircraft during the landing approach, the minimum altitude obtained during the abort landing maneuver is to be maximized. This maneuver is mathematically described by a Chebyshev optimal control problem. By a transformation to an optimal control problem of Mayer type, an additional state variable inequality constraint for the altitude has to be taken into account; here, its order is three. Due to this altitude constraint, the optimal trajectories exhibit, depending on the windshear parameters, up to four touch points and also up to one boundary arc at the minimum altitude level. The control variable is the angle of attack time rate which enters the equations of motion linearly; therefore, the Hamiltonian of the problem is nonregular. The switching structures also includes up to three singular subarcs and up to two boundary subarcs of an angle of attack constraint of first order. This structure can be obtained by applying some advanced necessary conditions of optimal control theory in combination with the multiple-shooting method. The optimal solutions exhibit an oscillatory behavior, reaching the minimum altitude level several times. By the optimization, the maximum survival capability can also be determined; this is the maximum wind velocity difference for which recovery from windshear is just possible. The computed optimal trajectories may serve as benchmark trajectories, both for guidance laws that are desirable to approach in actual flight and for optimal trajectories may then serve as benchmark trajectories both for guidance schemes and also for numerical methods for problems of optimal control. More... »

PAGES

21-57

References to SciGraph publications

  • 1987-11. Optimal abort landing trajectories in the presence of windshear in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1991-07. Abort landing in the presence of windshear as a minimax optimal control problem, part 1: Necessary conditions in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1991-07. Aircraft control for flight in an uncertain environment: Takeoff in windshear in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1993-04. Wind identification along a flight trajectory, part 3: 2D-dynamic approach in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1987-08. Quasi-steady flight to quasi-steady flight transition in a windshear: Trajectory optimization and guidance in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1974-08. A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting in NUMERISCHE MATHEMATIK
  • 1993. Introduction to Numerical Analysis in NONE
  • 1986-07. Guidance strategies for near-optimum take-off performance in a windshear in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1993-01. Wind identification along a flight trajectory, part 2: 2D-kinematic approach in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1986-04. Optimal take-off trajectories in the presence of windshear in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1988-08. Quasi-steady flight to quasi-steady flight transition for abort landing in a windshear: Trajectory optimization and guidance in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1991-08. Abort landing in the presence of windshear as a minimax optimal control problem, part 2: Multiple shooting and homotopy in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1992-10. Wind identification along a flight trajectory, part 1: 3D-kinematic approach in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1988-04. Optimal penetration landing trajectories in the presence of windshear in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1987-05. Maximum survival capability of an aircraft in a severe windshear in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
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    http://scigraph.springernature.com/pub.10.1007/bf02192298

    DOI

    http://dx.doi.org/10.1007/bf02192298

    DIMENSIONS

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