Optimal disturbance generation for flight control law testing

In this paper we present an approach for testing flight control laws with optimal disturbances using differential game theory. The approach is based on a state constrained differential game formulation in which the criterion under investigation is introduced in the cost function. In this differential game the first player representing disturbances acting on the closed loop system is trying to maximize the value of the criterion at a fixed terminal time point. For our application this player may not only model typical disturbances for flight control systems, such as wind gusts, but also pilot commands or other external influences which can drive the closed loop system to an unsafe state. The second, minimizing, player represents a control law parametrization and is subject to state constraints such as limits for actuator positions and rates. The value of this game provides a lower bound of the criterion under investigation for the given control structure and the bounded disturbances as well as the bounded parametrization of the control law. The numerical solution for this problem type is obtained by employing a highly parallelized solver implemented on a grid computer. The current implementation of this solver allows for the solution of nonlinear state constrained differential games in up to seven dimensions. An example problem formulation is presented for testing the longitudinal controller of a generic aircraft model using a worst case pilot command as disturbance input.