Certified Robust Invariant Polytope Training in Neural Controlled ODEs

Akash Harapanahalli, Samuel Coogan
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:982-999, 2026.

Abstract

We propose a framework for training neural network controllers with certified robust forward invariant polytopes. First, we parameterize a family of lifted control systems in a higher dimensional space, where the original neural controlled system evolves on an invariant subspace of each lifted system. We use interval analysis and neural network verifiers to further construct a family of lifted embedding systems, carefully capturing the knowledge of this invariant subspace. If the vector field of any lifted embedding system satisfies a sign constraint at a single point, then a certain convex polytope of the original system is robustly forward invariant. Treating the neural network controller and the lifted system parameters as variables, we propose an algorithm to train controllers with certified forward invariant polytopes in the closed-loop control system. Through two examples, we demonstrate how the simplicity of the sign constraint allows our approach to scale with system dimension to over $50$ states, and outperform state-of-the-art Lyapunov-based sampling approaches in runtime.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-harapanahalli26a, title = {Certified Robust Invariant Polytope Training in Neural Controlled ODEs}, author = {Harapanahalli, Akash and Coogan, Samuel}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {982--999}, 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/harapanahalli26a/harapanahalli26a.pdf}, url = {https://proceedings.mlr.press/v331/harapanahalli26a.html}, abstract = {We propose a framework for training neural network controllers with certified robust forward invariant polytopes. First, we parameterize a family of lifted control systems in a higher dimensional space, where the original neural controlled system evolves on an invariant subspace of each lifted system. We use interval analysis and neural network verifiers to further construct a family of lifted embedding systems, carefully capturing the knowledge of this invariant subspace. If the vector field of any lifted embedding system satisfies a sign constraint at a single point, then a certain convex polytope of the original system is robustly forward invariant. Treating the neural network controller and the lifted system parameters as variables, we propose an algorithm to train controllers with certified forward invariant polytopes in the closed-loop control system. Through two examples, we demonstrate how the simplicity of the sign constraint allows our approach to scale with system dimension to over $50$ states, and outperform state-of-the-art Lyapunov-based sampling approaches in runtime.} }
Endnote
%0 Conference Paper %T Certified Robust Invariant Polytope Training in Neural Controlled ODEs %A Akash Harapanahalli %A Samuel Coogan %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-harapanahalli26a %I PMLR %P 982--999 %U https://proceedings.mlr.press/v331/harapanahalli26a.html %V 331 %X We propose a framework for training neural network controllers with certified robust forward invariant polytopes. First, we parameterize a family of lifted control systems in a higher dimensional space, where the original neural controlled system evolves on an invariant subspace of each lifted system. We use interval analysis and neural network verifiers to further construct a family of lifted embedding systems, carefully capturing the knowledge of this invariant subspace. If the vector field of any lifted embedding system satisfies a sign constraint at a single point, then a certain convex polytope of the original system is robustly forward invariant. Treating the neural network controller and the lifted system parameters as variables, we propose an algorithm to train controllers with certified forward invariant polytopes in the closed-loop control system. Through two examples, we demonstrate how the simplicity of the sign constraint allows our approach to scale with system dimension to over $50$ states, and outperform state-of-the-art Lyapunov-based sampling approaches in runtime.
APA
Harapanahalli, A. & Coogan, S.. (2026). Certified Robust Invariant Polytope Training in Neural Controlled ODEs. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:982-999 Available from https://proceedings.mlr.press/v331/harapanahalli26a.html.

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