Measures and LMI for space launcher robust control validation

TL;DR

This paper introduces a novel verification framework using measure-based convex relaxations for analyzing the safety and robustness of nonlinear control laws in space launcher vehicles, addressing complex nonlinearities.

Contribution

It develops a measure-based convex relaxation approach for nonlinear robustness analysis, enabling efficient safety verification of space launcher control systems.

Findings

Successfully applied to space launcher benchmarks

Handles nonlinearities like saturations and dead-zones

Provides a scalable convex optimization framework

Abstract

We describe a new temporal verification framework for safety and robustness analysis of nonlinear control laws, our target application being a space launcher vehicle. Robustness analysis, formulated as a nonconvex nonlinear optimization problem on admissible trajectories corresponding to piecewise polynomial dynamics, is relaxed into a convex linear programming problem on measures. This infinite-dimensional problem is then formulated as a generalized moment problem, which allows for a numerical solution via a hierarchy of linear matrix inequality relaxations solved by semidefinite programming. The approach is illustrated on space launcher vehicle benchmark problems, in the presence of closed-loop nonlinearities (saturations and dead-zones) and axis coupling.