Aircraft take-off in windshear: A viability approach

This paper is devoted to the analysis of aircraft dynamics during take-off in the presence of windshear. We formulate the take-off problem as a differential game against Nature. Here, the first player is the relative angle of attack of the aircraft (considered as the control variable), and the second player is the disturbance caused by a windshear. We impose state constraints on the state variables of the game, which represents aircraft safety constraints (minimum altitude, given altitude rate). By using viability theory, we address the question of the existence of an open loop control assuring a viable trajectory (i.e., satisfying the state constraints) no matter what the disturbance is, i.e., for all admissible disturbances caused by the windshear. Through numerical simulations of the viability kernel algorithm, we demonstrate the capabilities of this approach for determining safe flight domains of an aircraft during take-off within windshear.