# An overview of the RFCS project V&V framework: optimization-based and linear tools for worst-case search Articles

• January 2015

• 303

• 318

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### International Standard Serial Number (ISSN)

• 18682502 (ISSN)

### abstract

• This article presents the application of nonlinear (simulation-based) and linear (structured singular value) worst-case tools to the VEGA launcher Verification and Validation process, during atmospheric ascent. The simulation-based worst-case evaluation is performed by minimizing a set of cost functions that capture the launcher¿s performance objectives, using the Worst-Case Analysis Optimization Tool and a high-fidelity nonlinear simulator of VEGA. The linear worst-case search uses the structured singular value ($$\mu$$¿) and a linear fractional transformation model representing the yaw rigid motion of the VEGA launcher but numerically evaluated using time simulation data from the VEGA simulator. To facilitate the analysis of the worst-case results as well as the comparison between the two analysis tools, a selection of the most critical uncertainties is performed using sensitivity analysis based on selected nonlinear simulator time responses. It is highlighted that the presented analysis tools are complementary to traditional Monte Carlo approaches in that they strive to identify worst-case uncertainty combinations as opposed to providing probabilistic guarantees on performance metric satisfaction. In addition, as it will be shown, these approaches require only a fraction of the time required to perform a Monte Carlo campaign. © 2015, CEAS.

### keywords

• lft model vega launcher verification & validation worst-case search ¿-analysis cost functions launching linear transformations mathematical transformations metadata monte carlo methods multivariable control systems sensitivity analysis simulators uncertainty analysis linear fractional transformations performance objective probabilistic guarantees structured singular values vega launcher verification-and-validation worst case evaluations worst-case search nonlinear analysis