Finite Horizon Worst Case Analysis of Linear Time-Varying Systems Applied to Launch Vehicle

Abstract

This article presents an efficient approach to compute the worst case gain of the interconnection of a finite time horizon linear time-varying system and a perturbation. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQCs). A condition for the worst case gain of such an interconnection can be formulated using dissipation theory as a parameterized Riccati differential equation, which depends on the chosen IQC multiplier. A nonlinear optimization problem is formulated to minimize the upper bound of the worst case gains over a set of admissible IQC multipliers. This problem can be efficiently solved with a custom-tailored logarithmically scaled, adaptive differential evolution algorithm. It provides a fast alternative to similar approaches based on solving semidefinite programs. The algorithm is applied to the worst case aerodynamic load analysis of an expendable launch vehicle (ELV). The worst case load of the uncertain ELV is calculated under wind turbulence during the atmospheric ascend and compared to results from nonlinear simulation.