Recursive Identification and Parameter Estimation

✍ Scribed by Han-Fu Chen, Wenxiao Zhao

• Publisher: CRC Press
• Year: 2014
• Tongue: English
• Leaves: 432
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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 Processes
Notes and References

Recursive Parameter Estimation
Parameter Estimation as Root-Seeking for Functions
Classical Stochastic Approximation Method: RM Algorithm
Stochastic Approximation Algorithm with Expanding Truncations
SAAWET with Nonadditive Noise
Linear Regression Functions
Convergence Rate of SAAWET
Notes and References

Recursive Identification for ARMAX Systems
LS and ELS for Linear Systems
Estimation Errors of LS/ELS
Hankel Matrices Associated with ARMA
Coefficient Identification of ARMAX by SAAWET
Order Estimation of ARMAX
Multivariate Linear EIV Systems
Notes and References

Recursive Identification for Nonlinear Systems
Recursive Identification of Hammerstein Systems
Recursive Identification of Wiener Systems
Recursive Identification of Wiener–Hammerstein Systems
Recursive Identification of EIV Hammerstein Systems
Recursive Identification of EIV Wiener Systems
Recursive Identification of Nonlinear ARX Systems
Notes and References

Other Problems Reducible to Parameter Estimation
Principal Component Analysis
Consensus of Networked Agents
Adaptive Regulation for Hammerstein and Wiener Systems
Convergence of Distributed Randomized PageRank Algorithms
Notes and References

Appendices:

Proof of Some Theorems in Chapter 1
Nonnegative Matrices

References
Index

✦ Subjects

Математика;Теория вероятностей и математическая статистика;Теория случайных процессов;