Solving Reachability Problems by a Scalable Constrained Optimization Method

TL;DR

This paper introduces a scalable constrained optimization approach to solve reachability problems in dynamical systems, efficiently handling non-uniqueness and exploiting problem structure for improved computational performance.

Contribution

It formulates a sparse, equality constrained nonlinear program for reachability, providing a scalable and efficient method that addresses solution non-uniqueness.

Findings

The method effectively solves reachability problems with sparse saddle-point matrices.

Comparison shows the proposed approach outperforms traditional line search and trust-region methods.

The approach handles non-uniqueness in solutions efficiently.

Abstract

In this paper we consider the problem of finding an evolution of a dynamical system that originates and terminates in given sets of states. However, if such an evolution exists then it is usually not unique. We investigate this problem and find a scalable approach for solving it. To this end we formulate an equality constrained nonlinear program that addresses the non-uniqueness of the solution of the original problem. In addition, the resulting saddle-point matrix is sparse. We exploit the structure in order to reach an efficient implementation of our method. In computational experiments we compare line search and trust-region methods as well as various updates for the Hessian.