Stochastic Approximation and Its Applications

2002
ISBN: 978-1-4020-0806-1
Verlag: Springer US

Buch, Englisch, Band 64, 360 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1570 g

Reihe: Nonconvex Optimization and Its Applications

Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application. For example, in system identification the unknown system coefficients are estimated on the basis of input-output data of the control system; in adaptive control systems the adaptive control gain should be defined based on observation data in such a way that the gain asymptotically tends to the optimal one; in blind ch- nel identification the channel coefficients are estimated using the output data obtained at the receiver; in signal processing the optimal weighting matrix is estimated on the basis of observations; in pattern classifi- tion the parameters specifying the partition hyperplane are searched by learning, and more examples may be added to this list. All these parameter estimation problems can be transformed to a root-seeking problem for an unknown function. To see this, let - note the observation at time i. e., the information available about the unknown parameters at time It can be assumed that the parameter under estimation denoted by is a root of some unknown function This is not a restriction, because, for example, may serve as such a function.

Zielgruppe

Research

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Produktionstechnik Fertigungstechnik
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Mikroprozessoren
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Robbins-Monro Algorithm.- Stochastic Approximation Algorithms with Expanding Truncations.- Asymptotic Properties of Stochastic Approximation Algorithms.- Optimization by Stochastic Approximation.- Application to Signal Processing.- Application to Systems and Control.