Optimal control based flight control law testing with parameter uncertainties

In the present paper we investigate a novel approach for optimal control based testing of flight control laws with respect to worst case pilot inputs, disturbances, such as wind gusts, and worst case parameter combinations. For the latter we consider parameters with fixed bounds, such as aircraft mass and statistically distributed parameters for the aerodynamic data set. In order to determine appropriate bounds on the statistically distributed parameters, first a maximum likelihood estimation problem is solved, utilizing measurements obtained via flight tests. This yields estimates of the considered parameters' mean and covariance matrix. Based on these quantities, the admissible set of the uncertain parameters for flight control law testing is then constrained to the respective 95% confidence region. This allows for the consideration of uncertainty due to the estimation algorithm by excluding unlikely parameter values in the optimal control problem. Furthermore, pilot inputs, wind gusts and parameters with fixed bounds are introduced as optimization variables. The approach is illustrated by testing the Angle-of-Attack protection of a modern twin engine aircraft w.r.t. worst case pilot load factor commands, wind gusts, and parametric uncertainties.