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

Identification of some nonlinear systems by using least-squares support vector machines

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 112-116.The well-known Wiener and Hammerstein type nonlinear systems and their various combinations are frequently used both in the modeling and the control of various electrical, physical, biological, chemical, etc... systems. In this thesis we will concentrate on the parametric identification and control of these type of systems. In literature, various identification methods are proposed for the identification of Hammerstein and Wiener type of systems. Recently, Least Squares-Support Vector Machines (LS-SVM) are also applied in the identification of Hammerstein type systems. In the majority of these works, the nonlinear part of Hammerstein system is assumed to be algebraic, i.e. memoryless. In this thesis, by using LS-SVM we propose a method to identify Hammerstein systems where the nonlinear part has a finite memory. For the identification of Wiener type systems, although various methods are also available in the literature, one approach which is proposed in some works would be to use a method for the identification of Hammerstein type systems by changing the roles of input and output. Through some simulations it was observed that this approach may yield poor estimation results. Instead, by using LS-SVM we proposed a novel methodology for the identification of Wiener type systems. We also proposed various modifications of this methodology and utilized it for some control problems associated with Wiener type systems. We also proposed a novel methodology for identification of NARX (Nonlinear Auto-Regressive with eXogenous inputs) systems. We utilize LS-SVM in our methodology and we presented some results which indicate that our methodology may yield better results as compared to the Neural Network approximators and the usual Support Vector Regression (SVR) formulations. We also extended our methodology to the identification of Wiener-Hammerstein type systems. In many applications the orders of the filter, which represents the linear part of the Wiener and Hammerstein systems, are assumed to be known. Based on LS-SVR, we proposed a methodology to estimate true ordersYavuzer, MahmutM.S

Topics in particle systems and singular SDEs

This thesis studies irregular stochastic (partial) differential equations arising in fluctuating hydrodynamics or regularization by noise, and homogenization limits thereof. In the first part, we consider a model for particles on a biological membrane. The membrane is given by an ultra-violet cutoff of the quasi-planar Helfrich surface, that is subject to space-time fluctuations. We study the homogenization limits of the Itô and Stratonovich rough paths lifts of the diffusion in different scaling regimes. As an outlook on the construction of the diffusion on the Helfrich membrane without cutoff, we prove convergence of the rescaled surface measures. Moreover, we study nonlinear approximations of the Dean-Kawasaki SPDE, a model for the dynamics of the empirical density of independent Brownian particles. We approximate this highly irregular SPDE such that the physical constraints of the particle system are preserved and derive weak error estimates. We prove well-posedness and a comparison principle for a class of nonlinear regularized Dean-Kawasaki equations. The second part of this thesis deals with the weak well-posedness of multidimensional singular SDEs with Besov drift in the rough regularity regime and additive stable jump noise. We first solve the associated fractional parabolic Kolmogorov equation. To that end, we employ the paracontrolled ansatz and furthermore generalize to irregular terminal conditions, that are itself paracontrolled. We then prove existence and uniqueness of a solution to the martingale problem. Motivated by the equivalence between probabilistic weak solutions of SDEs with bounded, measurable drift and solutions of the martingale problem, we define a rough-path-type weak solution concept for singular Lévy diffusions, proving moreover equivalence to the martingale solution in the Young and rough regime. To this end, we construct a rough stochastic sewing integral. In particular, we show that canonical weak solutions are in general non-unique in the rough case. We apply our theory to construct the Brox diffusion with Lévy noise. Finally, we combine the theory of periodic homogenization with the solution theory for singular SDEs with stable noise. For the martingale solution projected onto the torus, we prove existence of a unique invariant probability measure. We solve the singular Fokker-Planck equation and prove a strict maximum principle. Furthermore, we solve the singular resolvent and Poisson equation. Using Kipnis-Varadhan methods, we prove a central limit theorem and obtain a Brownian motion with constant diffusion matrix. In the pure stable noise case, we rescale differently and encounter no diffusivity enhancement. We conclude on the periodic homogenization result for the singular parabolic PDE via Feynman-Kac formula

Anwendung von maschinellem Lernen in der optischen Nachrichtenübertragungstechnik

Aufgrund des zunehmenden Datenverkehrs wird erwartet, dass die optischen Netze zukünftig mit höheren Systemkapazitäten betrieben werden. Dazu wird bspw. die kohärente Übertragung eingesetzt, bei der das Modulationsformat erhöht werden kann, erforder jedoch ein größeres SNR. Um dies zu erreichen, wird die optische Signalleistung erhöht, wodurch die Datenübertragung durch die nichtlinearen Beeinträchtigungen gestört wird. Der Schwerpunkt dieser Arbeit liegt auf der Entwicklung von Modellen des maschinellen Lernens, die auf diese nichtlineare Signalverschlechterung reagieren. Es wird die Support-Vector-Machine (SVM) implementiert und als klassifizierende Entscheidungsmaschine verwendet. Die Ergebnisse zeigen, dass die SVM eine verbesserte Kompensation sowohl der nichtlinearen Fasereffekte als auch der Verzerrungen der optischen Systemkomponenten ermöglicht. Das Prinzip von EONs bietet eine Technologie zur effizienten Nutzung der verfügbaren Ressourcen, die von der optischen Faser bereitgestellt werden. Ein Schlüsselelement der Technologie ist der bandbreitenvariable Transponder, der bspw. die Anpassung des Modulationsformats oder des Codierungsschemas an die aktuellen Verbindungsbedingungen ermöglicht. Um eine optimale Ressourcenauslastung zu gewährleisten wird der Einsatz von Algorithmen des Reinforcement Learnings untersucht. Die Ergebnisse zeigen, dass der RL-Algorithmus in der Lage ist, sich an unbekannte Link-Bedingungen anzupassen, während vergleichbare heuristische Ansätze wie der genetische Algorithmus für jedes Szenario neu trainiert werden müssen