# Application of the Free Energy Principle to Estimation and Control

arXiv: https://arxiv.org/abs/1910.09823 · HTML: https://mlsanity.com/paper/1910.09823/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2019.

## Built on by (most cited first, 5 of 5)

- [Active Inference in Robotics and Artificial Agents: Survey and Challenges](https://mlsanity.com/paper/2112.01871/) (2021)
- [Chance-Constrained Active Inference](https://mlsanity.com/paper/2102.08792/) (2021)
- [Information-seeking polynomial NARX model-predictive control through expected free energy minimization](https://mlsanity.com/paper/2312.15046/) (2023)
- [AIDA: An Active Inference-based Design Agent for Audio Processing Algorithms](https://mlsanity.com/paper/2112.13366/) (2021)
- [Active Inference for an Intelligent Agent in Autonomous Reconnaissance Missions](https://mlsanity.com/paper/2510.17450/) (2025)

## Abstract (arXiv)

Based on a generative model (GM) and beliefs over hidden states, the free energy principle (FEP) enables an agent to sense and act by minimizing a free energy bound on Bayesian surprise. Inclusion of prior beliefs in the GM about desired states leads to active inference (ActInf). In this work, we aim to reveal connections between ActInf and stochastic optimal control. We reveal that, in contrast to standard cost and constraint-based solutions, ActInf gives rise to a minimization problem that includes both an information-theoretic surprise term and a model-predictive control cost term. We further show under which conditions both methodologies yield the same solution for estimation and control. For a case with linear Gaussian dynamics and a quadratic cost, we illustrate the performance of ActInf under varying system parameters and compare to classical solutions for estimation and control.