# Stochastic Model and Optimal Control of an Active Tracking Particle with Information Processing

## TL;DR

This paper introduces a stochastic model of an active tracking particle with information processing, analyzing entropy, information flow, and optimal control to understand active systems with regulation and stochasticity.

## Contribution

It presents a novel stochastic model integrating information processing and control, providing insights into energy efficiency and optimal regulation strategies.

## Key findings

- Entropy production and information flow analyzed
- Optimal control strategies identified for energy and performance
- Model serves as a basis for understanding natural and artificial active systems

## Abstract

Living systems often function with regulatory interactions, but the question of how activity, stochasticity and regulations work together for achieving different goals still remains puzzling. We propose a stochastic model of an active tracking particle with information processing, where the entropy production and information flow are discussed, with the generalised fluctuation theorem serving as a benchmark for verifying the probability setup. Based on the model, the system performance, in terms of the first passage steps and the total energy consumption, are analysed in the variable space of (measurement error, control field), leading to discussions on optimal controls of the system. Not only elucidating the basic concepts involved in a stochastic active system with information processing, this prototypical model could also inspire more elaborated modelings of natural smart organisms and industrial designs of controllable active systems with desired physical performances in the future.