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.
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. - In: IFAC PAPERSONLINE. - ISSN 2405-8971. - ELETTRONICO. - 59:(2025), pp. 37-42. (Intervento presentato al convegno 6th IFAC Workshop on Linear Parameter Varying Systems LPVS 2025 tenutosi a Porto (Por) nel 2-4 July 2025) [10.1016/j.ifacol.2025.10.054].
A Scalable, Gradient-Stable Approach to Multi-Step, Nonlinear System Identification Using First-Order Methods
Cesare Donati;Martina Mammarella;Fabrizio Dabbene;Carlo Novara;
2025
Abstract
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.| File | Dimensione | Formato | |
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LPV2025_GRADIENT_FINAL.pdf
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1-s2.0-S2405896325014351-main.pdf
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https://hdl.handle.net/11583/3002383
