A scalable, gradient-stable approach to multi-step, nonlinear system identification using first-order methods
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917922030485504 |
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| author | Donati, Cesare Mammarella, Martina Dabbene, Fabrizio Novara, Carlo Lagoa, Constantino |
| author_facet | Donati, Cesare Mammarella, Martina Dabbene, Fabrizio Novara, Carlo Lagoa, Constantino |
| contents | This paper presents three main contributions to the field of multi-step system identification. First, drawing inspiration from Neural Network (NN) training, it introduces a tool for solving identification problems by leveraging first-order optimization and Automatic Differentiation (AD). The proposed method exploits gradients with respect to the parameters to be identified and leverages Linear Parameter-Varying (LPV) sensitivity equations to model gradient evolution. Second, it demonstrates that the computational complexity of the proposed method is linear in both the multi-step horizon length and the parameter size, ensuring scalability for large identification problems. Third, it formally addresses the "exploding gradient" issue: via a stability analysis of the LPV equations, it derives conditions for a reliable and efficient optimization and identification process for dynamical systems. Simulation results indicate that the proposed method is both effective and efficient, making it a promising tool for future research and applications in nonlinear system identification and non-convex optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A scalable, gradient-stable approach to multi-step, nonlinear system identification using first-order methods Donati, Cesare Mammarella, Martina Dabbene, Fabrizio Novara, Carlo Lagoa, Constantino Systems and Control This paper presents three main contributions to the field of multi-step system identification. First, drawing inspiration from Neural Network (NN) training, it introduces a tool for solving identification problems by leveraging first-order optimization and Automatic Differentiation (AD). The proposed method exploits gradients with respect to the parameters to be identified and leverages Linear Parameter-Varying (LPV) sensitivity equations to model gradient evolution. Second, it demonstrates that the computational complexity of the proposed method is linear in both the multi-step horizon length and the parameter size, ensuring scalability for large identification problems. Third, it formally addresses the "exploding gradient" issue: via a stability analysis of the LPV equations, it derives conditions for a reliable and efficient optimization and identification process for dynamical systems. Simulation results indicate that the proposed method is both effective and efficient, making it a promising tool for future research and applications in nonlinear system identification and non-convex optimization. |
| title | A scalable, gradient-stable approach to multi-step, nonlinear system identification using first-order methods |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2410.03544 |