Viability analysis of an aircraft flight domain for take-off in a windshear

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 (called viability constraints) on the game, namely minimum altitude constraints, which guarantee aircraft survival when encountering a windshear with given maximum intensity. By using viability theory, we address the question of 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 bounded disturbances. 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 windshears.