Learning-Based Resilient Interval Observers for Nonlinear Discrete-Time Bounded-Error Systems

Mareddu Siva Rohit, Parisa Ansari Bonab, Elisabeth Andarge Gedefaw, Mohammad Khajenejad
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1108-1120, 2026.

Abstract

This paper develops a unified framework for the synthesis of interval observers for nonlinear discrete-time systems with partially unknown dynamics and bounded noise. The proposed approach enables simultaneous state estimation and model identification by embedding a learning-based data-driven abstraction mechanism within an interval-observer structure. Specifically, the method integrates Jacobian sign-stable (JSS) decompositions and tight mixed-monotone decomposition functions with recursive data-driven over-approximations of the unknown dynamics. This integration yields tractable closed-form bounds for the learned models, which are iteratively refined using past interval framers, therefore ensuring both framer property and model adaptivity. In addition, observer gains are synthesized via a semidefinite programming (SDP) formulation that guarantees input-to-state stability and $\mathcal{H}_{\infty}$-optimality. Comprehensive simulations confirm that the proposed learning-augmented observer achieves accurate state and model estimation with significantly reduced computational complexity compared to previous optimization-based approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-rohit26a, title = {Learning-Based Resilient Interval Observers for Nonlinear Discrete-Time Bounded-Error Systems}, author = {Rohit, Mareddu Siva and Bonab, Parisa Ansari and Gedefaw, Elisabeth Andarge and Khajenejad, Mohammad}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1108--1120}, 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/rohit26a/rohit26a.pdf}, url = {https://proceedings.mlr.press/v331/rohit26a.html}, abstract = {This paper develops a unified framework for the synthesis of interval observers for nonlinear discrete-time systems with partially unknown dynamics and bounded noise. The proposed approach enables simultaneous state estimation and model identification by embedding a learning-based data-driven abstraction mechanism within an interval-observer structure. Specifically, the method integrates Jacobian sign-stable (JSS) decompositions and tight mixed-monotone decomposition functions with recursive data-driven over-approximations of the unknown dynamics. This integration yields tractable closed-form bounds for the learned models, which are iteratively refined using past interval framers, therefore ensuring both framer property and model adaptivity. In addition, observer gains are synthesized via a semidefinite programming (SDP) formulation that guarantees input-to-state stability and $\mathcal{H}_{\infty}$-optimality. Comprehensive simulations confirm that the proposed learning-augmented observer achieves accurate state and model estimation with significantly reduced computational complexity compared to previous optimization-based approaches.} }
Endnote
%0 Conference Paper %T Learning-Based Resilient Interval Observers for Nonlinear Discrete-Time Bounded-Error Systems %A Mareddu Siva Rohit %A Parisa Ansari Bonab %A Elisabeth Andarge Gedefaw %A Mohammad Khajenejad %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-rohit26a %I PMLR %P 1108--1120 %U https://proceedings.mlr.press/v331/rohit26a.html %V 331 %X This paper develops a unified framework for the synthesis of interval observers for nonlinear discrete-time systems with partially unknown dynamics and bounded noise. The proposed approach enables simultaneous state estimation and model identification by embedding a learning-based data-driven abstraction mechanism within an interval-observer structure. Specifically, the method integrates Jacobian sign-stable (JSS) decompositions and tight mixed-monotone decomposition functions with recursive data-driven over-approximations of the unknown dynamics. This integration yields tractable closed-form bounds for the learned models, which are iteratively refined using past interval framers, therefore ensuring both framer property and model adaptivity. In addition, observer gains are synthesized via a semidefinite programming (SDP) formulation that guarantees input-to-state stability and $\mathcal{H}_{\infty}$-optimality. Comprehensive simulations confirm that the proposed learning-augmented observer achieves accurate state and model estimation with significantly reduced computational complexity compared to previous optimization-based approaches.
APA
Rohit, M.S., Bonab, P.A., Gedefaw, E.A. & Khajenejad, M.. (2026). Learning-Based Resilient Interval Observers for Nonlinear Discrete-Time Bounded-Error Systems. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1108-1120 Available from https://proceedings.mlr.press/v331/rohit26a.html.

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