Structural Reformulations in System Identification.

• Superior document: Linköping Studies in Science and Technology. Dissertations Series ; v.1475
• Author: Lyzell, Christian.
• Place / Publishing House: Linköping : : Linkopings Universitet,, 2012.; {copy}2012.
• Year of Publication: 2012
• Edition: 1st ed.
• Language: English
• Series: Linköping Studies in Science and Technology. Dissertations Series
• Physical Description: 1 online resource (183 pages)

Table of Contents

• Intro
• Abstract
• Populärvetenskaplig sammanfattning
• Acknowledgments
• Contents
• Notation
• I Background
• 1 Introduction
• 1.1 Research Motivation
• 1.2 Outline of the Thesis
• 1.3 Contributions
• 2 System Identification
• 2.1 Introduction
• 2.2 Model Structures
• 2.2.1 Linear Time-Invariant
• 2.2.2 Nonlinear Time-Invariant
• 2.3 Instrumental Variables
• 2.4 Subspace Identification
• 2.4.1 Discrete Time
• 2.4.2 Continuous Time
• 2.5 An Algebraic Approach
• 2.6 Model Validation
• II Dimension Reduction
• 3 Introduction to Dimension Reduction
• 3.1 Introduction
• 3.2 System Identification Applications
• 3.3 Direct Regression Approaches
• 3.4 Inverse Regression Approaches
• 3.5 Summary
• 4 Inverse Regression for the Wiener Class of Systems
• 4.1 Introduction
• 4.2 Inverse Regression
• 4.3 Statistical Inference
• 4.4 Consistency Analysis
• 4.5 Local Linear Models
• 4.6 Simulations
• 4.6.1 Wiener Systems with a Single Branch
• 4.6.2 Wiener Systems with Multiple Branches
• 4.7 Concluding Remarks
• 4.A Complements
• 5 A Convex Relaxation of a Dimension Reduction Problem
• 5.1 Introduction
• 5.2 Minimum Average Variance Estimation
• 5.2.1 Design Choices
• 5.2.2 Dimension estimation
• 5.3 A Reformulation
• 5.4 A Convex Heuristic
• 5.5 Simulations
• 5.5.1 A Nonlinear Time Series
• 5.5.2 Wiener System with a Single Branch
• 5.5.3 Wiener System with Multiple Branches
• 5.6 Concluding Remarks
• 5.A The Adjoint Operator
• 5.B An Inverse Regression Formulation
• III Subspace Identification
• 6 Utilizing Structure Information in Subspace Identification
• 6.1 Introduction
• 6.2 OE Models
• 6.2.1 Discrete Time
• 6.2.2 Continuous Time
• 6.3 ARMAX Models
• 6.4 Special Gray-Box Models
• 6.5 Conclusions
• 7 Subspace Identification via Dimension Reduction
• 7.1 Introduction
• 7.2 Estimation Procedure.
• 7.3 Simulations
• 7.4 Conclusions
• IV Difference Algebra
• 8 Difference algebra and system identification
• 8.1 Introduction
• 8.2 Algebraic concepts
• 8.2.1 Signal shifts
• 8.2.2 Polynomials
• 8.2.3 Sets of polynomials
• 8.3 Identifiability
• 8.4 A pragmatic approach
• 8.5 Conclusions
• 9 Conclusions
• Bibliography.