A game theoretical approach to a flight test points distribution planning problem

In this paper we study the problem of the design of the test matrix for an envelope expansion test campaign, where both flutter and systems testing are required: the problem is to nd the optimal test points distribution in the admissible region, where each point represents specific data for a flight test. There are two dierent stakeholders involved: Structural Engineers (StE), who want to verify their predictions about the flutter free area, and Systems Engineers (SyE), who want to investigate environmental aspects in the entire operational flight envelope. The test matrix, representing the test points distribution in the flight envelope, i.e. the admissible region, can be found solving an optimization problem with hard constraints (flight envelope boundaries) and different objective functions for the two stakeholders: the aim of the StE is to optimize the distribution in Mach (M) range; the aim of SyE is to optimize the distribution in Pressure Altitude (H) range; both of them want to maximize test points density near maximum equivalent airspeed (VE) area. Given the goals of the two stakeholders, the problem is formulated as a two-player noncooperative game, where StE control M distribution and SyE control H distribution, according to their respective strategies. The two players, namely the StE and the SyE, make their decision about test points location simultaneously, playing a spatial competition game. Nash equilibrium solutions of the resulting game will represent the optimal test points distribution. For this game, existence results as well as computational aspects will be illustrated.