2021/12/31 by Alberto Bemporad, Bemporad, Alberto · 1 citation
Computer Science · Engineering · #Blind Source Separation Techniques #Control Systems and Identification #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Neural Networks and Applications #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2112.15348
openalex publication_date 2021/12/31 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
This paper proposes a novel algorithm for training recurrent neural network models of nonlinear dynamical systems from an input/output training dataset. Arbitrary convex and twice-differentiable loss functions and regularization terms are handled by sequential least squares and either a line-search (LS) or a trust-region method of Levenberg-Marquardt (LM) type for ensuring convergence. In addition, to handle non-smooth regularization terms such as ℓ1, ℓ0, and group-Lasso regularizers, as well as to impose possibly non-convex constraints such as integer and mixed-integer constraints, we combine sequential least squares with the alternating direction method of multipliers (ADMM). We call the resulting algorithm NAILS (nonconvex ADMM iterations and least squares) in the case line search (LS) is used, or NAILM if a trust-region method (LM) is employed instead. The training method, which is also applicable to feedforward neural networks as a special case, is tested in three nonlinear system identification problems.