Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910776411815936 |
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| author | Jaffe, Sean Davydov, Alexander Lapsekili, Deniz Singh, Ambuj Bullo, Francesco |
| author_facet | Jaffe, Sean Davydov, Alexander Lapsekili, Deniz Singh, Ambuj Bullo, Francesco |
| contents | Global stability and robustness guarantees in learned dynamical systems are essential to ensure well-behavedness of the systems in the face of uncertainty. We present Extended Linearized Contracting Dynamics (ELCD), the first neural network-based dynamical system with global contractivity guarantees in arbitrary metrics. The key feature of ELCD is a parametrization of the extended linearization of the nonlinear vector field. In its most basic form, ELCD is guaranteed to be (i) globally exponentially stable, (ii) equilibrium contracting, and (iii) globally contracting with respect to some metric. To allow for contraction with respect to more general metrics in the data space, we train diffeomorphisms between the data space and a latent space and enforce contractivity in the latent space, which ensures global contractivity in the data space. We demonstrate the performance of ELCD on the high dimensional LASA, multi-link pendulum, and Rosenbrock datasets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_08090 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees Jaffe, Sean Davydov, Alexander Lapsekili, Deniz Singh, Ambuj Bullo, Francesco Machine Learning Optimization and Control Global stability and robustness guarantees in learned dynamical systems are essential to ensure well-behavedness of the systems in the face of uncertainty. We present Extended Linearized Contracting Dynamics (ELCD), the first neural network-based dynamical system with global contractivity guarantees in arbitrary metrics. The key feature of ELCD is a parametrization of the extended linearization of the nonlinear vector field. In its most basic form, ELCD is guaranteed to be (i) globally exponentially stable, (ii) equilibrium contracting, and (iii) globally contracting with respect to some metric. To allow for contraction with respect to more general metrics in the data space, we train diffeomorphisms between the data space and a latent space and enforce contractivity in the latent space, which ensures global contractivity in the data space. We demonstrate the performance of ELCD on the high dimensional LASA, multi-link pendulum, and Rosenbrock datasets. |
| title | Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2402.08090 |