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arXiv · 2410.03544

A scalable, gradient-stable approach to multi-step, nonlinear system identification using first-order methods

Cesare Donati·Martina Mammarella·Fabrizio Dabbene·Carlo Novara·Constantino Lagoa
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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.

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Cesare Donati, Martina Mammarella, Fabrizio Dabbene, Carlo Novara, Constantino Lagoa. 2025-02-14. A scalable, gradient-stable approach to multi-step, nonlinear system identification using first-order methods. https://arxiv.org/abs/2410.03544

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