Estimation of Model Quality

Abstract This paper gives a survey and introduction to recent approaches to the problem of quantifying the errors in model estimation. Since this is such a large field we concentrate on approaches that have been motivated by the need for reliable models for control system design.

[1]  Y. F. Huang,et al.  On the value of information in system identification - Bounded noise case , 1982, Autom..

[2]  D.J.N. Limebeer,et al.  System identification for H/sup infinity / control , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[3]  L. Ljung,et al.  Hard frequency-domain model error bounds from least-squares like identification techniques , 1992 .

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

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

[6]  R. Kosut Adaptive control via parameter set estimation , 1988 .

[7]  S.M. Kay,et al.  Spectrum analysis—A modern perspective , 1981, Proceedings of the IEEE.

[8]  Abraham Wald,et al.  Asymptotic Properties of the Maximum Likelihood Estimate of an Unknown Parameter of a Discrete Stochastic Process , 1948 .

[9]  Graham C. Goodwin,et al.  UNCERTAINTY, INFORMATION AND ESTIMATION , 1990 .

[10]  Graham C. Goodwin,et al.  Some Observations on Robust Stochastic Estimation , 1988 .

[11]  E. Walter,et al.  Estimation of parameter bounds from bounded-error data: a survey , 1990 .

[12]  G. Goodwin,et al.  Quantification of Uncertainty in Estimation , 1990 .

[13]  T. H. Gronwall A sequence of polynomials connected with the $n$th roots of unity , 1921 .

[14]  J. Partington,et al.  Robust approximation and identification in H∞ , 1991, 1991 American Control Conference.

[15]  L. Ljung,et al.  Design variables for bias distribution in transfer function estimation , 1986, The 23rd IEEE Conference on Decision and Control.

[16]  Allan Pinkus,et al.  On the Erdös Conjecture Concerning Minimal Norm Interpolation on the Unit Circle , 1980 .

[17]  J. Partington Robust identification and interpolation in H , 1991 .

[18]  A. Helmicki,et al.  H∞ identification of stable LSI systems: a scheme with direct application to controller design , 1989, 1989 American Control Conference.

[19]  J. Norton Identification of parameter bounds for ARMAX models from records with bounded noise , 1987 .

[20]  C. N. Nett,et al.  Fundamentals of control-oriented system identification and their application for identification in H∞ , 1991, 1991 American Control Conference.

[21]  Guoxiang Gu,et al.  Identification in H∞ with nonuniformly spaced frequency response measurements , 1992, 1992 American Control Conference.

[22]  B. Hoadley Asymptotic Properties of Maximum Likelihood Estimators for the Independent Not Identically Distributed Case , 1971 .

[23]  Lennart Ljung,et al.  Model quality: the roles of prior knowledge and data information , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[24]  R. Tempo,et al.  Maximum likelihood estimators and worst case optimal algorithms for system identification , 1988 .

[25]  K. Hoffman Banach Spaces of Analytic Functions , 1962 .

[26]  Guoxiang Gu,et al.  A class of algorithms for identification in H∞ , 1992, Autom..

[27]  M. Milanese,et al.  Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors: Linear families of models and estimators , 1982 .

[28]  Jie Chen,et al.  Worst-case system identification in H∞: validation of apriori information, essentially optimal algorithms, and error bounds , 1992, 1992 American Control Conference.

[29]  F. Schweppe Recursive state estimation: Unknown but bounded errors and system inputs , 1967 .

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

[31]  Carl N. Nett,et al.  Control oriented system identification: a worst-case/deterministic approach in H/sub infinity / , 1991 .

[32]  P. L. Combettes The foundations of set theoretic estimation , 1993 .

[33]  Preston R. Clement Laguerre Functions in Signal Analysis and Parameter Identification , 1982 .

[34]  O. Bosgra,et al.  Approximate system identification using system based orthonormal functions , 1990, 29th IEEE Conference on Decision and Control.

[35]  L. Brutman On the Polynomial and Rational Projections in the Complex Plane , 1980 .

[36]  P. Erdos,et al.  An extremal problem in the theory of interpolation , 1964 .

[37]  L. Ljung,et al.  Asymptotic Properties of the Least Squares Method for Estimating Transfer Functions and Disturbance Spectra , 1992 .

[38]  Graham C. Goodwin,et al.  Estimated Transfer Functions with Application to Model Order Selection , 1992 .

[39]  J. P. Norton,et al.  Identification and application of bounded-parameter models , 1985, Autom..

[40]  Allan Pinkus,et al.  Proof of the conjectures of Bernstein and Erdös concerning the optimal nodes for polynomial interpolation , 1978 .

[41]  Bo Wahlberg,et al.  Approximate Modeling by Means of Orthonormal Functions , 1991 .

[42]  M. Crowder Maximum Likelihood Estimation for Dependent Observations , 1976 .

[43]  A. Helmicki,et al.  Identification in H∞: a robustly convergent, nonlinear algorithm , 1990, 1990 American Control Conference.

[44]  C. E. Rohrs,et al.  Identification with nonparametric uncertainty , 1992 .

[45]  Lennart Ljung,et al.  On Estimation of Transfer Function Error Bounds , 1991 .

[46]  E. Fogel System identification via membership set constraints with energy constrained noise , 1979 .

[47]  P. Khargonekar,et al.  Linear and nonlinear algorithms for identification in H∞ with error bounds , 1991, 1991 American Control Conference.

[48]  E. Cheney Introduction to approximation theory , 1966 .

[49]  Arthur J. Helmicki,et al.  Identification in H ∞ : linear algorithms , 1990 .

[50]  G. Goodwin,et al.  Quantification of Uncertainty in Estimation using an Embedding Principle , 1989 .

[51]  T. Sweeting Uniform Asymptotic Normality of the Maximum Likelihood Estimator , 1980 .

[52]  C. Jacobson,et al.  Worst Case System Identification in l1: Optimal Algorithms and Error Bounds , 1991, 1991 American Control Conference.

[53]  P. Caines,et al.  Asymptotic normality of prediction error estimators for approximate system models , 1980 .

[54]  László Gerencsér,et al.  Topics in Stochastic Systems: Modelling, Estimation, and Adaptive Control , 1991 .

[55]  Paul Erdös,et al.  Problems and results on the theory of interpolation. II , 1958 .

[56]  E. Walter,et al.  Exact recursive polyhedral description of the feasible parameter set for bounded-error models , 1989 .

[57]  G. Goodwin,et al.  A stochastic embedding approach for quantifying uncertainty in the estimation of restricted complexity models , 1989 .

[58]  J. Partington Robust identification in H , 1992 .

[59]  N. Young An Introduction to Hilbert Space , 1988 .

[60]  Robert Bitmead,et al.  Adaptive frequency response identification , 1987, 26th IEEE Conference on Decision and Control.

[61]  Pertti M. Mäkilä,et al.  Laguerre series approximation of infinite dimensional systems , 1990, Autom..

[62]  Beresford N. Parlett Some basic information on information-based complexity theory , 1992 .

[63]  P. Khargonekar,et al.  Linear and nonlinear algorithms for identification in H/sub infinity / with error bounds , 1992 .

[64]  Péter Vértesi,et al.  Optimal lebesgue constant for lagrange interpolation , 1990 .

[65]  Jonathan R. Partington,et al.  Approximation of delay systems by fourier-laguerre series , 1991, Autom..

[66]  Pramod P. Khargonekar,et al.  A comparison of classical stochastic estimation and deterministic robust estimation , 1992 .

[67]  Brett Ninness,et al.  Orthonormal Bases for Geometric Interpretations of the Frequency Response Estimation Problem , 1994 .

[68]  J. Deller Set membership identification in digital signal processing , 1989, IEEE ASSP Magazine.

[69]  John N. Tsitsiklis,et al.  Optimal asymptotic identification under bounded disturbances , 1993, IEEE Trans. Autom. Control..

[70]  R. Kosut Adaptive Robust Control via Transfer Function Uncertainty Estimation , 1988, 1988 American Control Conference.

[71]  Jonathan R. Partington,et al.  Algorithms for identification in H∞ with unequally spaced function measurements , 1993 .