Constrained similarity of 2-D trajectories by minimizing the H1 semi-norm of the trajectory difference

TL;DR

This paper introduces a method to measure and optimize the similarity between 2-D trajectories by minimizing the H1 semi-norm of their difference, with applications in mechanics and boundary value problems.

Contribution

It provides an exact solution for constrained trajectory similarity minimization using the H1 semi-norm, including a MATLAB implementation for practical use.

Findings

Exact solution for constrained trajectory similarity minimization.

Application to mechanics and boundary value problems.

MATLAB code provided for implementation.

Abstract

This paper defines constrained functional similarity between 2-D trajectories via minimizing the H1 semi-norm of the difference between the trajectories. An exact general solution is obtained for the case wherein the components of the trajectories are mesh-functions defined on a uniform mesh and the imposed constraints are linear. Various examples are presented, one of which features application to mechanics and two-point boundary value problems. A MATLAB code is given for the solution of one of the examples. The code could easily be adjusted to other cases.