Advances in Wireless Communications and Networks
Volume 3, Issue 6, November 2017, Pages: 75-83
Received: Oct. 5, 2017;
Accepted: Nov. 17, 2017;
Published: Dec. 5, 2017
Views 1168 Downloads 84
Hong Wang-Jian, School of Electronic Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou, China
Tang De-zhi, School of Electrical and Information Engineering, Anhui University of Technology, Ma-an-shan, China
In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.
Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation, Advances in Wireless Communications and Networks.
Vol. 3, No. 6,
2017, pp. 75-83.
Robust optimal experiment design for system identification
An optimal structure selection and parameter design approach for a dual-motor-driven system used in an electric bus
The spectral parameter estimation method for parameter identification of linear fractional order systems
Subspace identification and predictive control of batch particulate processes
Urban Forssel, Lennart Ljung, “Closed loop identification revisted,” Automatica, vol. 35, no. 7, pp. 1215-1241, 1999.
Ljung, L, “System identification: Theory for the user,” Prentice Hall, 1999.
Pintelon R, Schoukens J, “System identification: a frequency domain approach,” New York: IEEE Press, 2001.
Juan C, Augero, “A virtual closed loop method for closed loop identification,” Automatica, vol 47, no. 8, pp. 1626-1637, 2011.
U, Forssell, L Ljung, “Some results on optimal experiment design,” Automatica, vol 36, no. 5, pp. 749-756, 2000.
M, Leskers, “Closed loop identification of multivariable process with part of the inputs controlled,” International Journal of Control, vol 80, no. 10, pp. 1552-1561, 2007.
Hakan Hjalmarssion, “From experiment design to closed loop control,” Automatica, vol 41, no. 3, pp. 393-438, 2005,.
Hakan Hjalmarssion, “Closed loop experiment design for linear time invariant dynamical systems via LMI,” Automatica, vol 44, no. 3, pp. 623-636, 2008.
X, Bombois, “Least costly identification experiment for control,” Automatica, vol 42, no. 10, pp. 1651-1662, 2006.
Roland Hildebrand, “Identification for control: optimal input design with respect to a worst case gap cost function,” SIAM Journal of Control Optimization, vol 41, no. 5, pp. 1586-1608, 2003.
M, Gevers, “Identification of multi input systems: variance analysis and input design issues,” Automatica, vol 42, no.410, pp. 559-572, 2006.
M, Gevers, “Identification and information matrix: how to get just sufficiently rich,” IEEE Transactions on Automatic control, vol 54, no.12, pp. 2828-2840, 2009.
Graham C Goodin, “Bias issues in closed loop identification with application to adaptive control,” Communications in Information and Systems, vol 2, no.4, pp. 349-370, 2002.
James S Welsh, “Finite sample properties of indirect nonparametric closed loop identification,” IEEE Transactions on Automatic control, vol 47, no.8, pp. 1277-1291, 2002.
Sippe G Douma, “Validity of the standard cross correlation test for model structure validation,” Automatica, vol 44, no.4, pp. 1285-1294, 2008.
Wang Jian-hong, Wang Yan-xiang. “Model structure validation for closed loop system identification,” International Journal of Modelling, Identification and Control, vol 27, no.4, 323-331, 2017.
Balazs Cs Cgaji, “Sign perturbed sums: a new system identification approach for constructing exact non-asymptotic confidence region in linear regression models,”IEEE Transactions on Signal Processing, vol 69, no.1, pp. 169-181, 2015.
Scador Kolumhan, Istran Vajk, “Perturb data sets methods for hypothesis testing and structure of corresponding confidence sets,” Automatica, vol 51, no.1, pp. 326-331, 2015.
Michel Kieffer, Eric Walter, “Guaranteed characterization of exact non-asymptotic confidence regions as defined by LSCR and SPS,” Automatica, vol 50, no.2, pp. 507-512, 2014.