Automated Numerical Linearization for LFT Modelling Applied to Worst-Case Analysis of Launch Vehicles.

Abstract

Launch vehicles operate across highly dynamic flight regimes, where uncertainties in aerodynamics, structures, propulsion, and actuation critically affect performance and robustness. Classical robustness margins and Monte Carlo campaigns provide partial evidence but cannot ensure deterministic guarantees. Structured singular-value (µ) analysis can deliver such guarantees, yet its adoption is hindered by the challenge of generating Linear Fractional Transformation (LFT) models from complex nonlinear dynamics. This thesis develops a methodology that places numerical linearization at the core of the verification workflow. Compared to analytical derivations,often infeasible for large scale aerospace systems, numerical linearization is automatable, scalable across operating points, and directly compatible with industrial modelling practices. The proposed pipeline converts nonlinear subsystems into numerically linearized Linear Time Invariant (LTI) models, embeds structured uncertainties, and prepares them for robust analysis within the LFT framework. Two complementary validation steps are presented. On a representative toy example, the complete workflow—from nonlinear simulation to µ-analysis—is demonstrated, showing that deterministic worst-case evaluation can identify fragile perturbations not revealed by Monte Carlo sampling. In a simulation environment developed for the CALLISTO misson launcher model, the approach has been applied to selected subsystems, demonstrating that numerical linearization can be executed reliably and consistently in an industrial context, producing structured models suitable for subsequent robustness verification. Together, these results establish numerical linearization as a practical foundation for scalable LFT-based verification. While full µ-certification and complete subsystem coverage remain topics for future work, the methodology enables the systematic integration of deterministic robustness tools into launcher verification pipelines and provides a basis for hybrid deterministic–probabilistic clearance frameworks.