General duality between optimal control and estimation
Abstract
Optimal control and estimation are dual in the LQG setting, as Kalman discovered, however this duality has proven difficult to extend beyond LQG. Here we obtain a more natural form of LQG duality by replacing the Kalman-Bucy filter with the information filter. We then generalize this result to non-linear stochastic systems, discrete stochastic systems, and deterministic systems. All forms of duality are established by relating exponentiated costs to probabilities. Unlike the LQG setting where control and estimation are in one-to-one correspondence, in the general case control turns out to be a larger problem class than estimation and only a sub-class of control problems have estimation duals. These are problems where the Bellman equation is intrinsically linear. Apart from their theoretical significance, our results make it possible to apply estimation algorithms to control problems and vice versa.
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One can simulate active inference using generalisations of linear quadratic control or model predictive control.
“and one can simulate active inference using generalisations of linear quadratic control or model predictive control [93, 94]:”
From The free energy principle made simpler but not too simple (2023) · cites this paper as [94]
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References 17 · Cited by 248
- Authors
- Todorov, E.
- Affiliations
- University of California San Diego (US)
- Corresponding author
- Todorov, Emanuel
- Venue
- 2008 47th IEEE Conference on Decision and Control
- Publisher
- IEEE
- Published
- 2008
- Pages
- 4286-4292
- ISSN
- 0191-2216 (ISSN-L)
- OpenAlex
- W2155772159
- Cited by
- 248
- References
- 17
- Citations by year
- 2026: 6 · 2025: 11 · 2024: 14 · 2023: 16 · 2022: 18 · 2021: 30 · 2020: 34 · 2019: 23 · 2018: 20 · 2017: 11 · 2016: 7 · 2015: 7 · 2014: 8 · 2013: 9 · 2012: 8
- FWCI
- 6.43
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- IEEE Conference on Decision and Control (CDC) (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Target Tracking and Data Fusion in Sensor Networks
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
- Keywords
- optimal control, estimation, duality, LQG control, Kalman-Bucy filter, information filter, nonlinear stochastic systems, discrete stochastic systems, deterministic systems, Bellman equation
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