Learning Neural Network Controllers with Certified Robust Performance via Adversarial Training
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910094874116096 |
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| author | Junnarkar, Neelay Sonmez, Yasin Arcak, Murat |
| author_facet | Junnarkar, Neelay Sonmez, Yasin Arcak, Murat |
| contents | Neural network (NN) controllers achieve strong empirical performance on nonlinear dynamical systems, yet deploying them in safety-critical settings requires robustness to disturbances and uncertainty. We present a method for jointly synthesizing NN controllers and dissipativity certificates that formally guarantee robust closed-loop performance using adversarial training, in which we use counterexamples to the robust dissipativity condition to guide training. Verification is done post-training using alpha,beta-CROWN, a branch-and-bound-based method that enables direct analysis of the nonlinear dynamical system. The proposed method uses quadratic constraints (QCs) only for characterization of non-parametric uncertainties. The method is tested in numerical experiments on maximizing the volume of the set on which a system is certified to be robustly dissipative. Our method certifies regions up to 78 times larger than the region certified by a linear matrix inequality-based approach that we derive for comparison. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning Neural Network Controllers with Certified Robust Performance via Adversarial Training Junnarkar, Neelay Sonmez, Yasin Arcak, Murat Systems and Control Neural network (NN) controllers achieve strong empirical performance on nonlinear dynamical systems, yet deploying them in safety-critical settings requires robustness to disturbances and uncertainty. We present a method for jointly synthesizing NN controllers and dissipativity certificates that formally guarantee robust closed-loop performance using adversarial training, in which we use counterexamples to the robust dissipativity condition to guide training. Verification is done post-training using alpha,beta-CROWN, a branch-and-bound-based method that enables direct analysis of the nonlinear dynamical system. The proposed method uses quadratic constraints (QCs) only for characterization of non-parametric uncertainties. The method is tested in numerical experiments on maximizing the volume of the set on which a system is certified to be robustly dissipative. Our method certifies regions up to 78 times larger than the region certified by a linear matrix inequality-based approach that we derive for comparison. |
| title | Learning Neural Network Controllers with Certified Robust Performance via Adversarial Training |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.01188 |