Efficient State and Parameter Estimation of Nonlinear State-Space Models through Probabilistic Optimal Control

Victor Vantilborgh, Mohammad Mahmoudi Filabadi, Tom Lefebvre, Guillaume Crevecoeur
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1306-1321, 2026.

Abstract

This work presents a novel representation of the smoothing distribution - the posterior state distribution of a discrete-time dynamical system - through its connection to probabilistic optimal control. The key idea is to represent the posterior as the closed-loop behavior of a synthetic control system governed by an optimal stochastic policy. This formulation enables forward simulation of equally weighted trajectories that capture the statistics of the posterior without the need for backward sampling or importance weighting. We derive a practical algorithm based on probabilistic dynamic programming to compute this policy efficiently, with linear computational complexity in the number of particles. Furthermore, the uniform particle weighting significantly simplifies and accelerates the Expectation–Maximization algorithm, providing substantial benefits for system identification of nonlinear dynamical systems with latent states. The proposed method offers a simple, stable, and scalable alternative to traditional particle smoothers and demonstrates accurate parameter estimation and model learning at significantly reduced computational cost.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-vantilborgh26a, title = {Efficient State and Parameter Estimation of Nonlinear State-Space Models through Probabilistic Optimal Control}, author = {Vantilborgh, Victor and Filabadi, Mohammad Mahmoudi and Lefebvre, Tom and Crevecoeur, Guillaume}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1306--1321}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/vantilborgh26a/vantilborgh26a.pdf}, url = {https://proceedings.mlr.press/v331/vantilborgh26a.html}, abstract = {This work presents a novel representation of the smoothing distribution - the posterior state distribution of a discrete-time dynamical system - through its connection to probabilistic optimal control. The key idea is to represent the posterior as the closed-loop behavior of a synthetic control system governed by an optimal stochastic policy. This formulation enables forward simulation of equally weighted trajectories that capture the statistics of the posterior without the need for backward sampling or importance weighting. We derive a practical algorithm based on probabilistic dynamic programming to compute this policy efficiently, with linear computational complexity in the number of particles. Furthermore, the uniform particle weighting significantly simplifies and accelerates the Expectation–Maximization algorithm, providing substantial benefits for system identification of nonlinear dynamical systems with latent states. The proposed method offers a simple, stable, and scalable alternative to traditional particle smoothers and demonstrates accurate parameter estimation and model learning at significantly reduced computational cost.} }
Endnote
%0 Conference Paper %T Efficient State and Parameter Estimation of Nonlinear State-Space Models through Probabilistic Optimal Control %A Victor Vantilborgh %A Mohammad Mahmoudi Filabadi %A Tom Lefebvre %A Guillaume Crevecoeur %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-vantilborgh26a %I PMLR %P 1306--1321 %U https://proceedings.mlr.press/v331/vantilborgh26a.html %V 331 %X This work presents a novel representation of the smoothing distribution - the posterior state distribution of a discrete-time dynamical system - through its connection to probabilistic optimal control. The key idea is to represent the posterior as the closed-loop behavior of a synthetic control system governed by an optimal stochastic policy. This formulation enables forward simulation of equally weighted trajectories that capture the statistics of the posterior without the need for backward sampling or importance weighting. We derive a practical algorithm based on probabilistic dynamic programming to compute this policy efficiently, with linear computational complexity in the number of particles. Furthermore, the uniform particle weighting significantly simplifies and accelerates the Expectation–Maximization algorithm, providing substantial benefits for system identification of nonlinear dynamical systems with latent states. The proposed method offers a simple, stable, and scalable alternative to traditional particle smoothers and demonstrates accurate parameter estimation and model learning at significantly reduced computational cost.
APA
Vantilborgh, V., Filabadi, M.M., Lefebvre, T. & Crevecoeur, G.. (2026). Efficient State and Parameter Estimation of Nonlinear State-Space Models through Probabilistic Optimal Control. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1306-1321 Available from https://proceedings.mlr.press/v331/vantilborgh26a.html.

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