Structural Reformulations in System Identification

In system identification, the choice of model structure is important and it is sometimes desirable to use a flexible model structure that is able to approximate a wide range of systems. One such mo ...

[1]  Robert E. Mahony,et al.  Optimization Algorithms on Matrix Manifolds , 2007 .

[2]  Ker-Chau Li,et al.  On almost Linearity of Low Dimensional Projections from High Dimensional Data , 1993 .

[3]  K. Edström Switched Bond Graphs : Simulation and Analysis , 1999 .

[4]  M. Verhaegen,et al.  Identifying MIMO Wiener systems using subspace model identification methods , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[5]  Fredrik Gunnarsson,et al.  Uplink load in CDMA cellular radio systems , 2006, IEEE Transactions on Vehicular Technology.

[6]  Henrik Ohlsson,et al.  Regularization for Sparseness and Smoothness : Applications in System Identification and Signal Processing , 2010 .

[7]  P. Pucar,et al.  On the Hinge-Finding Algorithm for Hinging Hyperplanes , 1998, IEEE Trans. Inf. Theory.

[8]  Michael A. Saunders,et al.  LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares , 1982, TOMS.

[9]  R. Tibshirani Regression Shrinkage and Selection via the Lasso , 1996 .

[10]  M. Fliess,et al.  Nonlinear observability, identifiability, and persistent trajectories , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[11]  B. Wahlberg,et al.  Modelling and Identification with Rational Orthogonal Basis Functions , 2000 .

[12]  Christina Grönwall Ground Object Recognition using Laser Radar Data : Geometric Fitting, Performance Analysis, and Applications , 2006 .

[13]  Lexin Li,et al.  Sufficient dimension reduction via bayesian mixture modeling. , 2011, Biometrics.

[14]  B. Li,et al.  Dimension reduction for nonelliptically distributed predictors , 2009, 0904.3842.

[15]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[16]  Mikael Norrlöf,et al.  Iterative Learning Control : Analysis, Design, and Experiments , 2000 .

[17]  Tommy Svensson Mathematical Tools and Software for Analysis and Design of Nonlinear Control Systems , 1992 .

[18]  Stephen P. Boyd,et al.  A rank minimization heuristic with application to minimum order system approximation , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[19]  W. Rudin Principles of mathematical analysis , 1964 .

[20]  Daniel Axehill,et al.  Integer Quadratic Programming for Control and Communication , 2008 .

[21]  J. Sjöberg Optimal Control and Model Reduction of Nonlinear DAE Models , 2008 .

[22]  Han-Ming Wu Kernel Sliced Inverse Regression with Applications to Classification , 2008 .

[23]  R. Cook,et al.  Estimating the structural dimension of regressions via parametric inverse regression , 2001 .

[24]  Ali H. Sayed,et al.  Linear Estimation (Information and System Sciences Series) , 2000 .

[25]  R. Durrett Probability: Theory and Examples , 1993 .

[26]  R. Cook,et al.  Sufficient Dimension Reduction via Inverse Regression , 2005 .

[27]  Sun-Yuan Kung,et al.  A new identification and model reduction algorithm via singular value decomposition , 1978 .

[28]  Per-Johan Nordlund,et al.  Efficient Estimation and Detection Methods for Airborne Applications , 2008 .

[29]  Jeroen D. Hol,et al.  Sensor Fusion and Calibration of Inertial Sensors, Vision, Ultra-Wideband and GPS , 2011 .

[30]  Adam Krzyzak,et al.  A Distribution-Free Theory of Nonparametric Regression , 2002, Springer series in statistics.

[31]  Dietmar Bauer,et al.  Estimating ARMAX systems for multivariate time series using the state approach to subspace algorithms , 2009, J. Multivar. Anal..

[32]  B. Moor,et al.  Subspace identification for linear systems , 1996 .

[33]  Jonas Elbornsson,et al.  Analysis, Estimation and Compensation of Mismatch Effects in A/D Converters , 2003 .

[34]  Frida Eng,et al.  Non-Uniform Sampling in Statistical Signal Processing , 2007 .

[35]  Anders Helmersson,et al.  Methods for robust gain scheduling , 1995 .

[36]  S. Glad Solvability of differential algebraic equations and inequalities: An algorithm , 1997, 1997 European Control Conference (ECC).

[37]  R. Cook,et al.  Reweighting to Achieve Elliptically Contoured Covariates in Regression , 1994 .

[38]  Petre Stoica,et al.  Estimating Optimal Weights for Instrumental Variable Methods , 2001, Digit. Signal Process..

[39]  Gene H. Golub,et al.  Matrix computations , 1983 .

[40]  John W. Tukey,et al.  A Projection Pursuit Algorithm for Exploratory Data Analysis , 1974, IEEE Transactions on Computers.

[41]  S. Weisberg,et al.  Comments on "Sliced inverse regression for dimension reduction" by K. C. Li , 1991 .

[42]  S. Diop A state elimination procedure for nonlinear systems , 1989 .

[43]  Yingcun Xia,et al.  Sliced Regression for Dimension Reduction , 2008 .

[44]  H. Tong,et al.  An adaptive estimation of dimension reduction , 2002 .

[45]  T. Söderström On the uniqueness of maximum likelihood identification , 1975, Autom..

[46]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[47]  Yu Zhu,et al.  Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression , 2006 .

[48]  Michel Verhaegen,et al.  Filtering and System Identification: Frontmatter , 2007 .

[49]  M. L. Eaton A characterization of spherical distributions , 1986 .

[50]  Jiao Yang,et al.  Dimension estimation in sufficient dimension reduction: A unifying approach , 2011, J. Multivar. Anal..

[51]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[52]  J. Friedman Exploratory Projection Pursuit , 1987 .

[53]  Daniel Ankelhed,et al.  On design of low order H-infinity controllers , 2011 .

[54]  Michael I. Jordan,et al.  Kernel dimension reduction in regression , 2009, 0908.1854.

[55]  S. Andersson On Dimension Reduction in Sensor Array Signal Processing , 1992 .

[56]  Predrag Pucar Modeling and Segmentation using Multiple Models , 1995 .

[57]  Ragnar Wallin,et al.  Optimization Algorithms for System Analysis and Identification , 2004 .

[58]  Niclas Bergman,et al.  Recursive Bayesian Estimation : Navigation and Tracking Applications , 1999 .

[59]  S. Kotsios An application of Ritt’s remainder algorithm to discrete polynomial control systems , 2001 .

[60]  Abbas Emami-Naeini,et al.  Feedback Control of Dynamic Systems (6th edition) , 2010 .

[61]  R. Weiss,et al.  Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods , 2003 .

[62]  Lexin Li,et al.  Cluster-based estimation for sufficient dimension reduction , 2004, Comput. Stat. Data Anal..

[63]  Petre Stoica,et al.  MIMO system identification: state-space and subspace approximations versus transfer function and instrumental variables , 2000, IEEE Trans. Signal Process..

[64]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[65]  Lennart Ljung,et al.  Difference algebra and system identification , 2011, at - Automatisierungstechnik.

[66]  S. Kotsios,et al.  The model matching problem for a certain class of nonlinear systems , 1993 .

[67]  P. Misra,et al.  Numerically reliable computation of characteristic polynomials , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[68]  Jonathan R. Partington,et al.  On linear models for nonlinear systems , 2003, Autom..

[69]  J. Durbin EFFICIENT ESTIMATION OF PARAMETERS IN MOVING-AVERAGE MODELS , 1959 .

[70]  J. Ramos,et al.  A Null-Space-Based Technique for the Estimation of Linear-Time Invariant Structured State-Space Representations , 2012 .

[71]  H. Fortell Algebraic Approaches to Normal Forms and Zero Dynamics , 1995 .

[72]  J. Saracco,et al.  Cluster-based Sliced Inverse Regression , 2010 .

[73]  Yves Rolain,et al.  Parametric MIMO parallel Wiener identification , 2011, IEEE Conference on Decision and Control and European Control Conference.

[74]  Sette Diop,et al.  Elimination in control theory , 1991, Math. Control. Signals Syst..

[75]  G. Hendeby,et al.  Performance and Implementation Aspects of Nonlinear Filtering , 2008 .

[76]  K. Forsman Constructive Commutative Algebra in Nonlinear Control Theory , 1991 .

[77]  Rickard Karlsson,et al.  Particle filtering for positioning and tracking applications , 2005 .

[78]  Andreas Eidehall,et al.  Tracking and threat assessment for automotive collision avoidance , 2007 .

[79]  Lennart Ljung,et al.  NONLINEAR DYNAMICS IDENTIFIED BY MULTI-INDEX MODELS , 2005 .

[80]  T. Söderström,et al.  Instrumental variable methods for system identification , 1983 .

[81]  E. Kolchin Differential Algebra and Algebraic Groups , 2012 .

[82]  Bart Vandereycken,et al.  Low-Rank Matrix Completion by Riemannian Optimization , 2013, SIAM J. Optim..

[83]  A. Seidenberg An elimination theory for differential algebra , 1959 .

[84]  J. Löfberg Minimax approaches to robust model predictive control , 2003 .

[85]  Robin Sibson,et al.  What is projection pursuit , 1987 .

[86]  Ingela Lind,et al.  Regressor and Structure Selection Uses of ANOVA in System Identification , 2006 .

[87]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2009, Found. Comput. Math..

[88]  Michel Verhaegen,et al.  Filtering and System Identification: Kalman filtering , 2007 .

[89]  Svante Gunnarsson Frequency Domain Aspects of Modeling and Control in Adaptive Systems , 1988 .

[90]  Peng Zeng,et al.  An integral transform method for estimating the central mean and central subspaces , 2010, J. Multivar. Anal..

[91]  Urban Forssell Closed-loop Identification : Methods, Theory, and Applications , 1999 .

[92]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[93]  D. L. Hanson,et al.  On the strong law of large numbers for a class of stochastic processes , 1963 .

[94]  Ker-Chau Li,et al.  Sliced Inverse Regression for Dimension Reduction , 1991 .

[95]  Parikshit Shah,et al.  Linear system identification via atomic norm regularization , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[96]  B. Wahlberg On the Identification and Approximation of Linear Systems , 1987 .

[97]  J. Borwein,et al.  Convex Analysis And Nonlinear Optimization , 2000 .

[98]  Lennart Ljung,et al.  Estimate Physical Parameters by Black Box Modeling , 2003 .

[99]  Fredrik Tjärnström,et al.  Variance Expressions and Model Reduction in System Identification , 2002 .

[100]  Dietmar Bauer,et al.  ESTIMATING LINEAR DYNAMICAL SYSTEMS USING SUBSPACE METHODS , 2005, Econometric Theory.

[101]  Lieven Vandenberghe,et al.  Interior-Point Method for Nuclear Norm Approximation with Application to System Identification , 2009, SIAM J. Matrix Anal. Appl..

[102]  Christian Lundquist,et al.  Extended Target Tracking using a Gaussian-Mixture PHD Filter , 2017, IEEE Transactions on Aerospace and Electronic Systems.

[103]  J. Ritt Partial differential algebra , 1950 .

[104]  Christian Lundquist,et al.  Sensor fusion for automotive applications , 2011 .

[105]  Kjell Nordström Uncertainty, Robustness and Sensitivity Reduction in the Design of Single Input Control Systems , 1987 .

[106]  Martin Enqvist,et al.  A weighting method for approximate nonlinear system identification , 2007, 2007 46th IEEE Conference on Decision and Control.

[107]  Alberto Bemporad,et al.  Identification of piecewise affine systems via mixed-integer programming , 2004, Autom..

[108]  K. Fang,et al.  Asymptotics for kernel estimate of sliced inverse regression , 1996 .

[109]  P. Lindskog Methods, Algorithms and Tools for System Identification Based on Prior Knowledge , 1996 .

[110]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[111]  Johan A. K. Suykens,et al.  Nuclear norm regularization for overparametrized Hammerstein systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[112]  Mats Viberg,et al.  Subspace fitting concepts in sensor array processing , 1990 .

[113]  Jan-Erik Strömberg,et al.  A Mode Switching Modelling Philosophy , 1994 .

[114]  B. Wahlberg System identification using Laguerre models , 1991 .

[115]  Julian J. Bussgang,et al.  Crosscorrelation functions of amplitude-distorted gaussian signals , 1952 .

[116]  Jakob Roll Local and Piecewise Affine Approaches to System Identification , 2003 .

[117]  Magnus Larsson,et al.  Behavioral and Structural Model Based Approaches to Discrete Diagnosis , 1999 .

[118]  Berkant Savas,et al.  Rank reduction and volume minimization approach to state-space subspace system identification , 2006, Signal Process..

[119]  Vladimir Pavlovic,et al.  Central Subspace Dimensionality Reduction Using Covariance Operators , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[120]  Per Skoglar,et al.  Tracking and Planning for Surveillance Applications , 2012 .

[121]  B. Wahlberg System identification using Kautz models , 1994, IEEE Trans. Autom. Control..

[122]  Lennart Ljung,et al.  Estimating Linear Time-invariant Models of Nonlinear Time-varying Systems , 2001, Eur. J. Control.

[123]  A. Gut Probability: A Graduate Course , 2005 .

[124]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[125]  B. Bengtsson On some Control Problems for Queues , 1982 .

[126]  Xiangrong Yin,et al.  Sliced Inverse Regression with Regularizations , 2008, Biometrics.

[127]  S. Yun,et al.  An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems , 2009 .

[128]  Yingxing Li,et al.  On hybrid methods of inverse regression-based algorithms , 2007, Comput. Stat. Data Anal..

[129]  Valur Einarsson Model Checking Methods for Mode Switching Systems , 2000 .

[130]  Henrik Tidefelt,et al.  Differential-algebraic equations and matrix-valued singular perturbation , 2009 .

[131]  Lixing Zhu,et al.  Dimension Reduction in Regressions Through Cumulative Slicing Estimation , 2010 .

[132]  Allan Gut,et al.  An intermediate course in probability , 1995 .

[133]  Albert H. Nuttall Theory and application of the separable class of random processes , 1958 .

[134]  J. Friedman,et al.  Projection Pursuit Regression , 1981 .

[135]  Bruno Buchberger,et al.  A theoretical basis for the reduction of polynomials to canonical forms , 1976, SIGS.

[136]  Lennart Ljung,et al.  Handling Certain Structure Information in Subspace Identification , 2009 .

[137]  Jieping Ye,et al.  An accelerated gradient method for trace norm minimization , 2009, ICML '09.

[138]  Lixing Zhu,et al.  Asymptotics for sliced average variance estimation , 2007, 0708.0462.

[139]  Maarten Schoukens,et al.  Combining the Best Linear Approximation and Dimension Reduction to Identify the Linear Blocks of Parallel Wiener Systems , 2013, ALCOSP.

[140]  Lixing Zhu,et al.  Asymptotics of sliced inverse regression , 1995 .

[141]  L.R.J. Haverkamp,et al.  State space identification - Theory and practice , 2001 .

[142]  Stig Moberg,et al.  Modeling and Control of Flexible Manipulators , 2007 .

[143]  Yue-Ping Jiang,et al.  Recursive identification of MIMO Wiener systems with general inputs , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[144]  E. Bai An optimal two stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998 .

[145]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[146]  H. Luetkepohl The Handbook of Matrices , 1996 .

[147]  Johanna Wallén,et al.  Estimation-based iterative learning control , 2011 .

[148]  H. Akçay,et al.  An efficient frequency domain state-space identification algorithm , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[149]  David Törnqvist,et al.  Estimation and Detection with Applications to Navigation , 2008 .

[150]  Thomas M. Stoker,et al.  Investigating Smooth Multiple Regression by the Method of Average Derivatives , 2015 .

[151]  W. Härdle,et al.  Optimal Smoothing in Single-index Models , 1993 .

[152]  Paul Tseng,et al.  Hankel Matrix Rank Minimization with Applications to System Identification and Realization , 2013, SIAM J. Matrix Anal. Appl..

[153]  Shaoli Wang,et al.  On Directional Regression for Dimension Reduction , 2007 .

[154]  Martin S. Andersen,et al.  A convex relaxation of a dimension reduction problem using the nuclear norm , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[155]  Torsten Söderström,et al.  Discrete-time Stochastic Systems , 2002 .

[156]  Jonas Gillberg Frequency Domain Identification of Continuous-Time Systems : Reconstruction and Robustness , 2006 .

[157]  Lennart Ljung,et al.  Identification Aspects of Ritt's Algorithm for Discrete-Time Systems , 2009 .

[158]  Lennart Ljung,et al.  System identification toolbox for use with MATLAB , 1988 .

[159]  Liping Zhu,et al.  A Semiparametric Approach to Dimension Reduction , 2012, Journal of the American Statistical Association.

[160]  R. Irving,et al.  Integers, Polynomials, and Rings: A Course in Algebra , 2003 .

[161]  Petre Stoica,et al.  Spectral Analysis of Signals , 2009 .

[162]  G. Strang Introduction to Linear Algebra , 1993 .

[163]  R. Dennis Cook,et al.  Estimating central subspaces via inverse third moments , 2003 .

[164]  Håkan Hjalmarsson Aspects on Incomplete Modeling in System Identification , 1993 .

[165]  Inderjit S. Dhillon,et al.  Guaranteed Rank Minimization via Singular Value Projection , 2009, NIPS.

[166]  Bing Li,et al.  Dimension reduction for non-elliptically distributed predictors: second-order methods , 2010 .

[167]  Mille Millnert Identification and Control of Systems Subject to Abrupt Changes , 1983 .

[168]  Yitzhak Katznelson,et al.  A (terse) introduction to linear algebra , 2007 .

[169]  J. Sjöberg Non-Linear System Identification with Neural Networks , 1995 .

[170]  Hugues Garnier,et al.  Numerical illustrations of the relevance of direct continuous-time model identification , 2002 .

[171]  Christian Lyzell,et al.  Sliced Inverse Regression for the Identification of Dynamical Systems , 2012 .

[172]  Bo Wahlberg,et al.  Analysis of state space system identification methods based on instrumental variables and subspace fitting , 1997, Autom..

[173]  Y. Xia A constructive approach to the estimation of dimension reduction directions , 2007, math/0701761.

[174]  Lixing Zhu,et al.  Sufficient dimension reduction through discretization-expectation estimation , 2010 .

[175]  Xavier Bombois,et al.  Necessary and sufficient conditions for uniqueness of the minimum in Prediction Error Identification , 2012, Autom..

[176]  Liuping Wang,et al.  Identification of Continuous-time Models from Sampled Data , 2008 .

[177]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[178]  T. Glad,et al.  An Algebraic Approach to Linear and Nonlinear Control , 1993 .

[179]  Bart De Moor,et al.  Continuous-time frequency domain subspace system identification , 1996, Signal Process..

[180]  Alan Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[181]  Efstathia Bura Using linear smoothers to assess the structural dimension of regressions , 2001 .

[182]  Peter A. J. Nagy Tools for Knowledge-Based Signal Processing with Applications to System Identification , 1992 .

[183]  A. Tsybakov,et al.  Bandwidth Choice for Average Derivative Estimation , 1992 .

[184]  Anders Stenman,et al.  Model on Demand: Algorithms, Analysis and Applications , 1999 .

[185]  Guido De Roeck,et al.  Subspace identification of (AR)ARMAX, Box-Jenkins, and generalized model structures , 2009 .

[186]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

[187]  Christian Lyzell,et al.  Inverse Regression for the Wiener Class of Systems , 2012 .

[188]  David Williams,et al.  Probability with Martingales , 1991, Cambridge mathematical textbooks.

[189]  J. Gunnarsson Symbolic Methods and Tools for Discrete Event Dynamic Systems , 1997 .

[190]  M. Fliess Automatique en temps discret et algèbre aux différences , 1990 .

[191]  Tao Wang,et al.  Sparse sufficient dimension reduction using optimal scoring , 2013, Comput. Stat. Data Anal..

[192]  Inger Klein,et al.  Automatic Synthesis of Sequential Control Schemes , 1993 .

[193]  Lennart Ljung,et al.  Adaptive control based on explicit criterion minimization , 1985, Autom..

[194]  Lixing Zhu,et al.  On Sliced Inverse Regression With High-Dimensional Covariates , 2006 .

[195]  E. Bai,et al.  Block Oriented Nonlinear System Identification , 2010 .

[196]  Bo Wahlberg,et al.  A linear regression approach to state-space subspace system identification , 1996, Signal Process..

[197]  T. McKelvey Identification of State-Space Models from Time and Frequency Data , 1995 .

[198]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[199]  H. Zha,et al.  Contour regression: A general approach to dimension reduction , 2005, math/0508277.

[200]  M. Jirstrand Constructive Methods for Inequality Constraints in Control , 1998 .

[201]  Ker-Chau Li,et al.  On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma , 1992 .

[202]  Ke Wang-Chen Transformation and Symbolic Calculations in Filtering and Control , 1994 .

[203]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[204]  M. Schetzen The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[205]  R. Dennis Cook,et al.  A note on shrinkage sliced inverse regression , 2005 .

[206]  H. Jonson A Newton Method for Solving Non-Linear Optimal Control Problems with General Constraints , 1983 .

[207]  S. Glad Implementing Ritt’s Algorithm of Differential Algebra , 1992 .

[208]  A. Isaksson On System Identification in one and two Dimensions with Signal Processing Applications , 1988 .

[209]  F. Gustafsson Estimation of Discrete Parameters in Linear Systems , 1993 .

[210]  Fredrik Gunnarsson Power control in cellular radio system: Analysis, design and estimation , 2000 .

[211]  Heinz Kredel,et al.  Gröbner Bases: A Computational Approach to Commutative Algebra , 1993 .

[212]  Liping Zhu,et al.  On kernel method for sliced average variance estimation , 2007 .