Aircraft take-off in windshear: A viability approach
The authors analyze aircraft dynamics during takeoff in the presence of windshear. They formulate this problem in terms of a differential game against Nature. In this formulation the first player controls the angle of attack against the disturbance due to windshear, which plays the role of the second player. In this situation one have to take into account state constraints corresponding to safety obligations. Using viability theory, the authors numerically obtain an approximation of the domain of initial positions from which there exists at least one trajectory, and an associated control loop, which satisfies the safety constraints. The state variables are the horizontal and vertical coordinates or the aircraft, the relative speed, the relative path inclination and the relative angle of attack. Windshear disturbances are wind speed and its time derivative. The control variable is the derivative of the angle of attack. Numerical issues are given for a 4-D model. Using the discriminating kernel algorithm which is an extension to differential games of the viability kernel algorithm, the authors calculate the set of initial flight conditions for which there exists viable trajectories no matter what the windshear intensity are.
scientific article; zbMATH DE number 1523582