Efficient Encoding of Dynamical Systems through Local Approximations

TL;DR

This paper introduces a novel method for efficiently encoding dynamical systems by combining local models with states, inspired by the MDL principle, to reduce communication in networked control systems.

Contribution

It develops a new local approximation-based encoding method for dynamical systems, addressing the gap in efficient representations compared to static data.

Findings

Effective encoding reduces communication in event-triggered state estimation

Method demonstrates efficiency across various dynamical systems

Supports improved data exchange in networked control systems

Abstract

An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as classification, regression, or decision making. However, the representation of dynamical systems has received less attention. In this work, we develop a method to represent a dynamical system efficiently as a combination of a state and a local model, which fulfills a criterion inspired by the minimum description length (MDL) principle. The MDL principle is used in machine learning and statistics to quantify the trade-off between the ability to explain seen data and the model complexity. Networked control systems are a prominent example, where such a representation is beneficial. When many agents share a network, information exchange is costly and should thus happen only when necessary. We empirically show the efficiency of the proposed encoding for several dynamical systems and demonstrate reduced communication for event-triggered state estimation problems.