Berkmann, P.; Pesch, H. J. Abort landing in windshear: Optimal control problem with third-order state constraint and varied switching structure. (English) Zbl 0827.49027 J. Optimization Theory Appl. 85, No. 1, 21-57 (1995). Summary: 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 structure 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 pilot training in flight simulators. They are computed for a realistic windshear model, taking into account the possible presence of updraft/downdraft regions associated with low-altitude windshears accompanied by vortices. Cited in 7 Documents MSC: 49N70 Differential games and control 49N75 Pursuit and evasion games 49J35 Existence of solutions for minimax problems Keywords:windshear-downburst models; nonregular Hamiltonian; multipoint boundary- value problems; abort landing; Chebyshev optimal control problem; problem of Mayer type; state variable inequality constraint; boundary arc; necessary conditions; multiple-shooting method Software:BNDSCO PDFBibTeX XMLCite \textit{P. Berkmann} and \textit{H. J. Pesch}, J. Optim. Theory Appl. 85, No. 1, 21--57 (1995; Zbl 0827.49027) Full Text: DOI References: [1] Long, M. 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