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.