Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 2: Numerical Computations

TL;DR

This paper presents numerical methods for approximating the minimum time function in linear control systems using reachable set approximations, including error analysis and handling cases with discontinuous or Hölder continuous functions.

Contribution

It introduces an algorithm for numerical approximation of the minimum time function via reachable sets, with error estimates and applicability to non-smooth cases.

Findings

Higher order convergence in certain cases

Effective approximation for discontinuous minimum time functions

Demonstrated differences with other numerical methods

Abstract

In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other numerical approaches we provide a collection of numerical examples which either allow higher order of convergence with respect to time discretization or where the continuity of the minimum time function cannot be sufficiently granted, i.e. we study cases in which the minimum time function is H\"older continuous or even discontinuous.