Finite Horizon Worst Case Analysis of Launch Vehicles *

摘要

This paper presents a robust linear time varying (LTV) analysis of a space launcher. It evaluates the worst case aerodynamic loads during the atmospheric flight phase under wind turbulence. The results of the LTV analysis are evaluated against a Monte Carlo simulation of the respective industry-sized nonlinear launcher model over a set of allowable uncertainties and disturbances. The recent extension of the strict/ finite horizon bounded real lemma (BRL) for integral quadratic constraints is applied, covering the robustness analysis of finite horizon linear time varying (LTV) systems. Here, an equivalent formulation of the strict BRL in the form of a Riccati differential equality (RDE) is used. The RDEs direct dependence on the IQC multiplier leads to a nonlinear optimization problem, which can be solved efficiently. Using this, it is possible to explicitly respect the time varying dynamics of the space launcher in the worst case analysis. Furthermore, the incorporation of IQCs opens the analysis to a broader range of analyzable perturbations.