An L-BFGS-B approach for linear and nonlinear system identification under $\ell_1$ and group-Lasso regularization
This provides a more efficient and stable tool for engineers and researchers in control systems and robotics, though it is incremental as it adapts existing optimization techniques to system identification.
The paper tackles system identification for linear and nonlinear state-space models by proposing an L-BFGS-B-based method with regularization, showing it often outperforms classical linear subspace methods in results, generality, and numerical stability, and applies it to an industrial robot benchmark.
In this paper, we propose a very efficient numerical method based on the L-BFGS-B algorithm for identifying linear and nonlinear discrete-time state-space models, possibly under $\ell_1$ and group-Lasso regularization for reducing model complexity. For the identification of linear models, we show that, compared to classical linear subspace methods, the approach often provides better results, is much more general in terms of the loss and regularization terms used (such as penalties for enforcing system stability), and is also more stable from a numerical point of view. The proposed method not only enriches the existing set of linear system identification tools but can also be applied to identifying a very broad class of parametric nonlinear state-space models, including recurrent neural networks. We illustrate the approach on synthetic and experimental datasets and apply it to solve a challenging industrial robot benchmark for nonlinear multi-input/multi-output system identification. A Python implementation of the proposed identification method is available in the package jax-sysid, available at https://github.com/bemporad/jax-sysid.