{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-kalman-bucy-filters-linear-quadratic","title":"On Kalman-Bucy filters, linear quadratic control and active inference","arxiv_id":"2005.06269","date":"2020-05-13","proceeding":null,"authors":[],"abstract":"Linear Quadratic Gaussian (LQG) control is a framework first introduced in\ncontrol theory that provides an optimal solution to linear problems of\nregulation in the presence of uncertainty. This framework combines Kalman-Bucy\nfilters for the estimation of hidden states with Linear Quadratic Regulators\nfor the control of their dynamics. Nowadays, LQG is also a common paradigm in\nneuroscience, where it is used to characterise different approaches to\nsensorimotor control based on state estimators, forward and inverse models.\nAccording to this paradigm, perception can be seen as a process of Bayesian\ninference and action as a process of optimal control. Recently, active\ninference has been introduced as a process theory derived from a variational\napproximation of Bayesian inference problems that describes, among others,\nperception and action in terms of (variational and expected) free energy\nminimisation. Active inference relies on a mathematical formalism similar to\nLQG, but offers a rather different perspective on problems of sensorimotor\ncontrol in biological systems based on a process of biased perception. In this\nnote we compare the mathematical treatments of these two frameworks for linear\nsystems, focusing on their respective assumptions and highlighting their\ncommonalities and technical differences.","url_abs":"http://arxiv.org/abs/2005.06269v1","url_pdf":"http://arxiv.org/pdf/2005.06269v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"on-kalman-bucy-filters-linear-quadratic","repo_url":"https://github.com/mbaltieri/GeneralisedFiltering","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}