Solving Underdetermined Boundary Value Problems By Sequential Quadratic Programming

TL;DR

This paper introduces an algorithm using sequential quadratic programming and multiple shooting to find trajectories in ordinary differential equations that reach dangerous states, aiding in system safety analysis.

Contribution

It presents a novel application of sequential quadratic programming combined with multiple shooting for solving boundary value problems in system safety.

Findings

The algorithm effectively finds trajectories reaching specified states.

It demonstrates robustness in handling underdetermined boundary value problems.

The method improves safety verification processes.

Abstract

Ordinary differential equations that model technical systems often contain states, that are considered dangerous for the system. A trajectory that reaches such a state usually indicates a flaw in the design. In this paper, we present and study the properties of an algorithm for finding such trajectories. That is, for a given ordinary differential equation, the algorithm finds a trajectory that originates in one set of states and reaches another one. The algorithm is based on sequential quadratic programming applied to a regularized optimization problem obtained by multiple shooting.