Identification of linear continuous-time systems under irregular and random output sampling

This paper considers the problem of identifiability and parameter estimation of single-input-single-output, linear, time-invariant, stable, continuous-time systems under irregular and random sampling schemes. Conditions for system identifiability are established under inputs of exponential polynomial types and a tight bound on sampling density. Identification algorithms of Gauss-Newton iterative types are developed to generate convergent estimates. When the sampled output is corrupted by observation noises, input design, sampling times, and convergent algorithms are intertwined. Persistent excitation (PE) conditions for strongly convergent algorithms are derived. Unlike the traditional identification, the PE conditions under irregular and random sampling involve both sampling times and input values. Under the given PE conditions, iterative and recursive algorithms are developed to estimate the original continuous-time system parameters. The corresponding convergence results are obtained. Several simulation examples are provided to verify the theoretical results.

[1]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[2]  Hyunjoong Kim,et al.  Functional Analysis I , 2017 .

[3]  Vasile I. Istrăţescu,et al.  Fixed point theory : an introduction , 1981 .

[4]  M. B. Zarrop,et al.  Book Review: Computer Controlled Systems: theory and design (3rd Ed.) , 1998 .

[5]  Fernando Paganini,et al.  IEEE Transactions on Automatic Control , 2006 .

[6]  Keith R. Godfrey,et al.  Direct and indirect least squares methods in continuous-time parameter estimation , 1987, Autom..

[7]  Charles R. Phillips,et al.  Digital control system analysis and design , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  R. Jennrich.  Asymptotic Properties of Non-Linear Least Squares Estimators , 1969 .

[9]  H. Teicher,et al.  Probability theory: Independence, interchangeability, martingales , 1978 .

[10]  Rolf Johansson.  Continuous-Time Model Identification and State Estimation Using Non-Uniformly Sampled Data , 2009 .

[11]  Magnus Mossberg.  High-Accuracy Instrumental Variable Identification of Continuous-Time Autoregressive Processes From Irregularly Sampled Noisy Data , 2008, IEEE Transactions on Signal Processing.

[12]  Minyue Fu,et al.  A Continuous-Time Linear System Identification Method for Slowly Sampled Data , 2010, IEEE Transactions on Signal Processing.

[13]  C. Desoer,et al.  Global inverse function theorem , 1972 .

[14]  C. Berenstein.  Complex Analysis and Special Topics in Harmonic Analysis , 1995 .

[15]  G. Goodwin,et al.  Identification of continuous-time state-space models from non-uniform fast-sampled data , 2011 .

[16]  Torsten Söderström,et al.  Identification of continuous-time AR processes from unevenly sampled data , 2002, Autom..

[17]  Carlos S. Kubrusly,et al.  Stochastic approximation algorithms and applications , 1973, CDC 1973.

[18]  K. Deimling.  Fixed Point Theory , 2008 .

[19]  Fredrik Gustafsson,et al.  Event based sampling with application to vibration analysis in pneumatic tires , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[20]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[21]  Le Yi Wang,et al.  Joint state and event observers for linear switching systems under irregular sampling , 2013, Autom..

[22]  G. Yin,et al.  System Identification with Quantized Observations , 2010 .

[23]  I. Sandberg.  Global inverse function theorems , 1980 .

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

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

[26]  Andreu Mas-Colell,et al.  Homeomorphisms of Compact, Convex Sets and the Jacobian Matrix , 1979 .

[27]  Le Yi Wang,et al.  State Observability and Observers of Linear-Time-Invariant Systems Under Irregular Sampling and Sensor Limitations , 2011, IEEE Transactions on Automatic Control.

[28]  Lennart Ljung,et al.  Frequency domain identification of continuous-time output error models, Part II: Non-uniformly sampled data and B-spline output approximation , 2010, Autom..

[29]  Feng Ding,et al.  Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems , 2009, Autom..

[30]  Torsten Söderström,et al.  Identification of Continuous-Time ARX Models From Irregularly Sampled Data , 2007, IEEE Transactions on Automatic Control.

[31]  Stephen A. Dyer,et al.  Digital signal processing , 2018, 8th International Multitopic Conference, 2004. Proceedings of INMIC 2004..

[32]  Yucai Zhu,et al.  System Identification using Slow and Irregular Output Samples , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[33]  K. Åström,et al.  Comparison of Periodic and Event Based Sampling for First-Order Stochastic Systems , 1999 .