Bridging the gap between linear and nonlinear worst-case analysis: an application case to the atmospheric phase of the VEGA launcher

This article presents the application of the structured singular value worst-case approach to the VEGA launcher during the atmospheric ascent phase. The analysis uses a linear fractional transformation model, formed from a subset of the uncertainty and dispersion parameters defined for the nonlinear VEGA system, to identify physically feasible worst-cases. This analysis is complementary to traditional Monte Carlo campaigns in that it provides an analytical guaranteed existence of worst-case conditions. To exemplify the difference, a dense (100,000 runs) Monte Carlo campaign in a high-fidelity VEGA nonlinear simulator yielded no performance-violating cases but, the results presented show that the application of mu-analysis is capable of identifying numerous parametric uncertainty combinations away from the extremes resulting in performance violations in the same VEGA nonlinear simulator at a fraction of the computational time. Thus, the present application shows that linear analytical approaches such as mu-analysis (when supported by proper development of a linear fractional transformation model) have capabilities that complement the traditional design verification and validation process for launchers.