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

TL;DR

This paper introduces a novel, efficient method for worst-case gain analysis of finite horizon linear time-varying systems with uncertainties, applied to launch vehicle aerodynamic load assessment.

Contribution

It formulates a Riccati differential equation-based condition for worst-case gain and develops a tailored optimization algorithm, offering a faster alternative to semidefinite programming methods.

Findings

Successfully applied to launch vehicle aerodynamic load analysis.

Achieved faster computation compared to traditional SDP-based methods.

Validated results against nonlinear simulations.

Abstract

This paper presents an approach to compute the worst-case gain of the interconnection of a finite time horizon linear time-variant 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 gain over a set of admissible IQC multipliers. This problem can be efficiently solved with a custom-tailored logarithm 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 for 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.