Identifying Single-Input Linear System Dynamics from Reachable Sets

TL;DR

This paper introduces a method to identify linear system dynamics solely from observed reachable sets over time, without needing individual trajectories, applicable to various system dimensions and input conditions.

Contribution

It demonstrates that reachable sets uniquely determine system dynamics under certain conditions and provides an algorithm for practical identification.

Findings

Reachable sets can uniquely determine system dynamics for asymmetric inputs.

The method applies to systems of any dimension under generic assumptions.

An algorithm successfully identified a band-pass filter circuit from reachable set data.

Abstract

This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the reachable sets are known from partially transparent manufacturer specifications or observations of the collective behavior of adversarial agents, we aim to utilize such sets to determine the unknown system's dynamics. This paper has two contributions. Firstly, we show that the sequence of the system's reachable sets can be used to uniquely determine the system's dynamics for asymmetric input sets under some generic assumptions, regardless of the system's dimensions. We also prove the same property holds up to a sign change for two-dimensional systems where the input set is symmetric around zero. Secondly, we present an algorithm to determine these dynamics. We apply and verify the developed theory and algorithms on an unknown band-pass filter circuit solely provided the unknown system's reachable sets over a finite observation period.