Application of the Free Energy Principle to Estimation and Control
Journal article, 2021

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, i.e., the negative logarithm of the marginal likelihood. Inclusion of desired states in the form of prior beliefs in the GM 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.

Optimal control

factor graphs

Probabilistic logic

Probability density function


Numerical models

stochastic optimal control

Stochastic processes

Active inference

Signal processing

message passing


Thijs van de Laar

Eindhoven University of Technology

Ayca Ozcelikkale

Uppsala University

Henk Wymeersch

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

IEEE Transactions on Signal Processing

1053-587X (ISSN)

Vol. 69 4234-4244

Multi-dimensional Signal Processing with Frequency Comb Transceivers

Swedish Research Council (VR) (2018-03701), 2018-12-01 -- 2021-12-31.

Smart Sensing and Communications with Energy Harvesting

Swedish Research Council (VR) (2015-04011), 2016-01-01 -- 2019-12-31.

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering



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5/4/2022 3