Fundamental limitations on the accuracy of MIMO linear models obtained by PEM for systems operating in open loop

In this paper we show that the variance of estimated parametric models for open loop Multiple-Input Multiple-Output (MIMO) systems obtained by the prediction error method (PEM) satisfies a fundamental integral limitation. The fundamental limitation gives rise to a multivariable `waterbed' effect.

[1]  Brett Ninness,et al.  Integral constraints on the accuracy of least-squares estimation , 1996, Autom..

[2]  Cristian R. Rojas,et al.  Fundamental Limitations on the Variance of Estimated Parametric Models , 2009, IEEE Transactions on Automatic Control.

[3]  Xavier Bombois,et al.  Least costly identification experiment for control , 2006, Autom..

[4]  Graham C. Goodwin,et al.  Qualitative aspects of the distribution of errors in least squares estimation , 1990, at - Automatisierungstechnik.

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

[6]  B. Ninness,et al.  The Waterbed Effect in Spectral Estimation , 2004, IEEE Signal Processing Magazine.

[7]  L. Ljung,et al.  Black-box identification of multivariable transfer functions—asymptotic properties and optimal input design , 1984 .

[8]  Håkan Hjalmarsson,et al.  The fundamental role of general orthonormal bases in system identification , 1999, IEEE Trans. Autom. Control..

[9]  Andrew Harvey,et al.  The econometric analysis of time series , 1991 .

[10]  Håkan Hjalmarsson,et al.  Input design via LMIs admitting frequency-wise model specifications in confidence regions , 2005, IEEE Transactions on Automatic Control.

[11]  Graham C. Goodwin,et al.  L2-overbiased, L2-underbiased and L2-unbiased estimation of transfer functions , 1994, Autom..

[12]  André Klein,et al.  A generalization of Whittle's formula for the information matrix of vector-mixed time series , 2000 .

[13]  G. Goodwin,et al.  EXPERIMENT DESIGN FOR TIME SERIES ANALYSIS: THE MULTIVARIATE CASE* , 1979 .

[14]  Graham C. Goodwin,et al.  Choosing Between Open- and Closed-Loop Experiments in Linear System Identification , 2007, IEEE Transactions on Automatic Control.

[15]  P. Caines.  Linear Stochastic Systems , 1988 .

[16]  L. Ljung.  Asymptotic variance expressions for identified black-box transfer function models , 1984 .

[17]  Benjamin Friedlander,et al.  A general lower bound for parametric spectrum estimation , 1984 .

[18]  Michel Gevers,et al.  Identification of multi-input systems: variance analysis and input design issues , 2006, Autom..

[19]  Håkan Hjalmarsson,et al.  From experiment design to closed-loop control , 2005, Autom..

[20]  Graham C. Goodwin,et al.  Control System Design , 2000 .

[21]  W. E. Larimore,et al.  A Survey of Some Recent Developments in System Parameter Identification , 1982 .

[22]  Yucai Zhu.  Black-box identification of mimo transfer functions: Asymptotic properties of prediction error models , 1989 .

[23]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[24]  D.G. Dudley,et al.  Dynamic system identification experiment design and data analysis , 1979, Proceedings of the IEEE.

[25]  P. Spreij,et al.  Matrix differential calculus applied to multiple stationary time series and an extended Whittle formula for information matrices , 2009 .

[26]  Guy Melard,et al.  The information matrix of multiple-input single-output time series models , 1994 .

[27]  L. Ljung.  Convergence analysis of parametric identification methods , 1978 .

[28]  Dennis S. Bernstein,et al.  Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory , 2005 .

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

[30]  Victor Solo,et al.  Topics in advanced time series analysis , 1986 .

[31]  D. Cox,et al.  Parameter Orthogonality and Approximate Conditional Inference , 1987 .