Probabilistic ODE Solvers for Integration Error-Aware Numerical Optimal Control
(2024) 6th Annual Learning for Dynamics and Control Conference, L4DC 2024 In Proceedings of Machine Learning Research 242. p.1018-1032- Abstract
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting accuracy and sampling time requirements simultaneously can be challenging using classical discretization methods. In particular, neither fixed-grid nor adaptive-grid discretizations may be suitable, when they suffer from large integration error or exceed the prescribed sampling time, respectively. In this work, we take a first step at closing this gap by utilizing probabilistic numerical integrators to approximate the solution of the initial value problem, as well as the computational uncertainty... (More)
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting accuracy and sampling time requirements simultaneously can be challenging using classical discretization methods. In particular, neither fixed-grid nor adaptive-grid discretizations may be suitable, when they suffer from large integration error or exceed the prescribed sampling time, respectively. In this work, we take a first step at closing this gap by utilizing probabilistic numerical integrators to approximate the solution of the initial value problem, as well as the computational uncertainty associated with it, inside the optimal control problem (OCP). By taking the viewpoint of probabilistic numerics and propagating the numerical uncertainty in the cost, the OCP is reformulated such that the optimal input reduces the computational uncertainty insofar as it is beneficial for the control objective. The proposed approach is illustrated using a numerical example, and potential benefits and limitations are discussed.
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- author
- Lahr, Amon ; Tronarp, Filip LU ; Bosch, Nathanael ; Schmidt, Jonathan ; Hennig, Philipp and Zeilinger, Melanie N.
- organization
- publishing date
- 2024
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- nonlinear model predictive control, numerical integration, probabilistic numerics
- in
- Proceedings of Machine Learning Research
- volume
- 242
- pages
- 15 pages
- publisher
- ML Research Press
- conference name
- 6th Annual Learning for Dynamics and Control Conference, L4DC 2024
- conference location
- Oxford, United Kingdom
- conference dates
- 2024-07-15 - 2024-07-17
- external identifiers
-
- scopus:85203696615
- ISSN
- 2640-3498
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2024 A. Lahr, F. Tronarp, N. Bosch, J. Schmidt, P. Hennig & M.N. Zeilinger.
- id
- 244fd7f4-2fef-4f90-803f-9e39ebbd9ee8
- alternative location
- https://proceedings.mlr.press/v242/lahr24a.html
- date added to LUP
- 2024-12-10 09:20:00
- date last changed
- 2025-04-04 14:35:37
@article{244fd7f4-2fef-4f90-803f-9e39ebbd9ee8,
abstract = {{<p>Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting accuracy and sampling time requirements simultaneously can be challenging using classical discretization methods. In particular, neither fixed-grid nor adaptive-grid discretizations may be suitable, when they suffer from large integration error or exceed the prescribed sampling time, respectively. In this work, we take a first step at closing this gap by utilizing probabilistic numerical integrators to approximate the solution of the initial value problem, as well as the computational uncertainty associated with it, inside the optimal control problem (OCP). By taking the viewpoint of probabilistic numerics and propagating the numerical uncertainty in the cost, the OCP is reformulated such that the optimal input reduces the computational uncertainty insofar as it is beneficial for the control objective. The proposed approach is illustrated using a numerical example, and potential benefits and limitations are discussed.</p>}},
author = {{Lahr, Amon and Tronarp, Filip and Bosch, Nathanael and Schmidt, Jonathan and Hennig, Philipp and Zeilinger, Melanie N.}},
issn = {{2640-3498}},
keywords = {{nonlinear model predictive control; numerical integration; probabilistic numerics}},
language = {{eng}},
pages = {{1018--1032}},
publisher = {{ML Research Press}},
series = {{Proceedings of Machine Learning Research}},
title = {{Probabilistic ODE Solvers for Integration Error-Aware Numerical Optimal Control}},
url = {{https://proceedings.mlr.press/v242/lahr24a.html}},
volume = {{242}},
year = {{2024}},
}