Application of the Free Energy Principle to Estimation and Control

Thijs W. van de Laar (Corresponding author), Ayca Ozcelikkale, Henk Wymeersch

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Article number9478190
Pages (from-to)4234-4244
Number of pages11
JournalIEEE Transactions on Signal Processing
Early online date8 Jul 2021
Publication statusPublished - 2021


  • Active inference
  • factor graphs
  • message passing
  • stochastic optimal control


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