Regularized system identification. Learning dynamic models from data
This monograph focuses on comprehensive overview of the most common type of the inverse problems: system identification (SI). It organized as follows. First, authors introduce the SI's roots from statistical theory dealing with classic system identification, and introduce the general tools and terms such bias, variance, cross-validation as well as black-box and gray-box models. Next, regularization of linear regression models is considered with focus mainly on the least squares method and its regularization. Next chapter deals with Bayesian interpretation of regularization including popular Markov chain Monte Carlo estimation. Then, after historical introduction and motivation for regularization methods for linear system identification (in ``classical'' mean square error perspective), authors focuses on the linear system identification and regularization in reproducing kernel Hilbert spaces and support vector machines. Here the special attention is paid to kernels examples. Finally, before moving to cases studies, authors deals with regularization for nonlinear system identification. The special attention is paid to the Bayesian estimation of Gaussian random fields, Volterra and deep learning models of nonlinear dynamical systems. Finally, numerical experiments and real world cases (including biomedical and mechanics applications) are discussed.
scientific article; zbMATH DE number 7488353