Regularized System Identification

This open access book provides a comprehensive treatment of recent developments in kernel-based identification that are of interest to anyone engaged in learning dynamic systems from data. The reader is led step by step into understanding of a novel paradigm that leverages the power of machine learning without losing sight of the system-theoretical principles of black-box identification. The authors’ reformulation of the identification problem in the light of regularization theory not only offers new insight on classical questions, but paves the way to new and powerful algorithms for a variety of linear and nonlinear problems. Regression methods such as regularization networks and support vector machines are the basis of techniques that extend the function-estimation problem to the estimation of dynamic models. Many examples, also from real-world applications, illustrate the comparative advantages of the new nonparametric approach with respect to classic parametric prediction error methods. The challenges it addresses lie at the intersection of several disciplines so Regularized System Identification will be of interest to a variety of researchers and practitioners in the areas of control systems, machine learning, statistics, and data science. This is an open access book

Improved Distributed Estimation Method for Environmental\ud time-variant Physical variables in Static Sensor Networks

In this paper, an improved distributed estimation scheme for static sensor networks is developed. The scheme is developed for environmental time-variant physical variables. The main contribution of this work is that the algorithm in [1]-[3] has been extended, and a filter has been designed with weights, such that the variance of the estimation errors is minimized, thereby improving the filter design considerably\ud and characterizing the performance limit of the filter, and thereby tracking a time-varying signal. Moreover, certain parameter optimization is alleviated with the application of a particular finite impulse response (FIR) filter. Simulation results are showing the effectiveness of the developed estimation algorithm

Regularization and Bayesian Learning in Dynamical Systems: Past, Present and Future

Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use of regularization in system identification has evolved over the years, starting from the early contributions both in the Automatic Control as well as Econometrics and Statistics literature. In particular we shall discuss some fundamental issues such as compound estimation problems and exchangeability which play and important role in regularization and Bayesian approaches, as also illustrated in early publications in Statistics. The historical and foundational issues will be given more emphasis (and space), at the expense of the more recent developments which are only briefly discussed. The main reason for such a choice is that, while the recent literature is readily available, and surveys have already been published on the subject, in the author's opinion a clear link with past work had not been completely clarified.Comment: Plenary Presentation at the IFAC SYSID 2015. Submitted to Annual Reviews in Contro

Least third-order cumulant method with adaptive regularization parameter selection for neural networks

AbstractThis paper introduces an interesting property of the least third-order cumulant objective function. The property is that the solution is optimal when the gradients of Mean Squares error and third-order cumulant error are zero vectors. The optimal solutions are independent of the value of regularization parameter λ. Also, an adaptive regularization parameter selection method is derived to control the convergences of Mean Squares error and the cumulant error terms. The proposed selection method is able to tunnel through the sub-optimal solutions, of which the locations are controllable, via changing the value of the regularization parameter. Consequently, the least third-order cumulant method with the adaptive regularization parameter selection method is theoretically capable of estimating an optimal solution when it is applied to regression problems