Recursive Identification and Parameter Estimation

Recursive Identification and Parameter Estimation describes a recursive approach to solving system identification and parameter estimation problems arising from diverse areas. Supplying rigorous theoretical analysis, it presents the material and proposed algorithms in a manner that makes it easy to understand—providing readers with the modeling and identification skills required for successful theoretical research and effective application.The book begins by introducing the basic concepts of probability theory, including martingales, martingale difference sequences, Markov chains, mixing processes, and stationary processes. Next, it discusses the root-seeking problem for functions, starting with the classic RM algorithm, but with attention mainly paid to the stochastic approximation algorithms with expanding truncations (SAAWET) which serves as the basic tool for recursively solving the problems addressed in the book.The book not only identifies the results of system identification and parameter estimation, but also demonstrates how to apply the proposed approaches for addressing problems in a range of areas, including: Identification of ARMAX systems without imposing restrictive conditions Identification of typical nonlinear systems Optimal adaptive tracking Consensus of multi-agents systems Principal component analysis Distributed randomized PageRank computation This book recursively identifies autoregressive and moving average with exogenous input (ARMAX) and discusses the identification of non-linear systems. It concludes by addressing the problems arising from different areas that are solved by SAAWET. Demonstrating how to apply the proposed approaches to solve problems across a range of areas, the book is suitable for students, researchers, and engineers working in systems and control, signal processing, communication, and mathematical statistics.

Dependent Random Vectors Some Concepts of Probability Theory Independent Random Variables, Martingales, and Martingale Difference Sequences Markov Chains with State Space (Rm;Bm)Mixing Random Processes Stationary ProcessesNotes and ReferencesRecursive Parameter Estimation Parameter Estimation as Root-Seeking for FunctionsClassical Stochastic Approximation Method: RM AlgorithmStochastic Approximation Algorithm with Expanding Truncations SAAWET with Nonadditive NoiseLinear Regression Functions Convergence Rate of SAAWETNotes and References Recursive Identification for ARMAX SystemsLS and ELS for Linear SystemsEstimation Errors of LS/ELSHankel Matrices Associated with ARMACoefficient Identification of ARMAX by SAAWETOrder Estimation of ARMAXMultivariate Linear EIV SystemsNotes and ReferencesRecursive Identification for Nonlinear SystemsRecursive Identification of Hammerstein SystemsRecursive Identification of Wiener SystemsRecursive Identification of Wiener–Hammerstein SystemsRecursive Identification of EIV Hammerstein SystemsRecursive Identification of EIV Wiener SystemsRecursive Identification of Nonlinear ARX SystemsNotes and ReferencesOther Problems Reducible to Parameter Estimation Principal Component AnalysisConsensus of Networked AgentsAdaptive Regulation for Hammerstein and Wiener SystemsConvergence of Distributed Randomized PageRank AlgorithmsNotes and ReferencesAppendices: Proof of Some Theorems in Chapter 1Nonnegative MatricesReferencesIndex

Han-Fu Chengraduated from the Leningrad (St. Petersburg) State University and joined the Institute of Mathematics, Chinese Academy of Sciences (CAS). Since 1979, he has been with the Institute of Systems Science, being now a part of the Academy of Mathematics and Systems Science, CAS. He is a professor of the Key Laboratory of Systems and Control of CAS. His research interests are mainly in stochastic systems, including system identification, adaptive control, and stochastic approximation and its applications to systems, control, and signal processing. He authored and coauthored more than 200 journal papers and seven books.Han-Fu Chen served as an IFAC Council member (2002–2005), president of the Chinese Association of Automation (1993–2002), and a permanent member of the Council of the Chinese Mathematics Society (1991–1999). He is an IEEE fellow, IFAC fellow, a member of TWAS, and a member of CAS. Wenxiao Zhao received his BSc degree from the Department of Mathematics, Shandong University, China in 2003 and the PhD degree from the Institute of Systems Science, AMSS, the Chinese Academy of Sciences (CAS) in 2008. After this he was a postdoctoral student at the Department of Automation, Tsinghua University. During this period he visited the University of Western Sydney, Australia, for nine months. Then, Dr. Zhao joined the Institute of SystemsSciences, CAS in 2010. He now is with the Key Laboratory of Systems and Control, CAS as an associate professor. His research interests are in system identification, adaptive control, and system biology. He serves as the general secretary of the IEEE Control Systems Beijing Chapter and an associate editor of the Journal of Systems Science and Mathematical Sciences