Robust flight control system design verification and validation by multiobjective worst-case search

The flight control law design verification and validation (DVV) problem can be formulated as a robustness analysis problem, where a set of suitably defined evaluation criteria must be checked to lie within certain limits for all admissible variations of vehicle parameters, external inputs and all flight conditions. The idea of optimization based worst case DVV is to use available and efficient optimization methods to find those parameters/ inputs/flight conditions for which the criteria are violated or poorly satisfied. The potentials of this approach are its general usability for both frequency-domain and timedomain analysis, and for both linear and non-linear models and control laws including complex non-linearity. Moreover, there is no limitation on the number of parametric uncertainties that can be investigated and the method does not itself add conservatism to the clearance problem as many other alternatives do, mainly those based on approximations or simplifications. The most challenging problem with the optimization based approach is to confidently assert that no violation exists for all parameters/ inputs/flight conditions thus a global optimization problem has to be solved. This usually results in a huge amount of computational work. Newer global optimization strategies like non-dominating sorting genetic algorithms can solve non-convex and non-smooth single and multiobjective optimization problems. Solving worst case problems as a multiobjective problem can help to reduce computational effort otherwise necessary for multiple single criteria optimizations. Moreover, the set of Pareto-optimal solutions of a multiobjective optimization problem can give more insight into correlations between different requirements. The DVV process based on multiobjective optimization is demonstrated on a nonlinear six degrees of freedom time domain simulation model of the VEGA launcher including thrust vector control. Eight evaluation criteria are considered evaluating aerodynamic load, lateral drift and separation requirements in the first flight phase. The Pareto-optimal results are presented and the according worst cases are compared to single objective optimization and Monte-Carlo analysis results. A strategy to confidently identify regions of compliance by means of a sequence of optimizations will also be proposed.