Abort Landing of an Airplane under Different Windshear Conditions: An Optimal Control Problem with a Third-Order State Constraint and a Multifarious Switching Structure

. 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 inadvertently 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 which is of order three here. 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 of the level of minimum altitude. The control variable is the angle of attack rate which enters the equations of motion linearly. Therefore, the Hamiltonian of the problem is nonregular. The complicated switching structures wh..