Abstract
Based on the assumption of Unknown-But–Bounded (UBB) noise, an interval algorithm is presented for set-membership parameter identification of a multiple-input multiple-output (MIMO) linear time-invariant (LTI) system. By virtue of interval mathematics, the objective of this study is to seek the minimal interval estimation (or hyper-rectangle) of parameters to be identified, which is compatible with the measured data and the bounded noise. The present algorithm can obtain not only the center estimations of parameters, but also the bounds of errors on them. Numerical example is used to illustrate its small computation efforts and higher accuracy by comparison with Fogel’s ellipsoidal algorithm and the least squares algorithm.
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References
Fogel, E.: System identification via membership set constraints with energy constrained noise. IEEE Transactions on Automatic Control AC 24(5), 752–758 (1979)
Fogel, E., Huang, Y.F.: On the value of information in system identification-Bounded noise case. Automatica 18(2), 229–238 (1982)
Milanese, M., Belforte, G.: Estimation theory and uncertainty intervals evaluation in present of unknown but bounded errors: Linear families of models and estimators. IEEE Transactions on Automatic Control AC 27(2), 408–414 (1982)
Cerone, V.: Feasible parameter set for linear models with bounded errors in all variables. Automatica 29(6), 1551–1555 (1993)
Sun, X.F.: Set membership identification-Algorithm, Convergence, Robustness. (Ph D Thesis). Institute of Automation, Chinese Academy of Sciences Beijing (1994) (in Chinese)
Yue, Z.J.: Near-optimal input design for set-membership identification. Journal of PLA University of Science and Technology 2(2), 96–98 (2001) (in Chinese)
Garrido, R., Miranda, R.: DC servomechanism parameter identification: A closed loop input error approach. ISA Transactions 51(1), 42–49 (2012)
Li, L., Liu, W.Y., Han, B.: Dynamical level set method for parameter identification of nonlinear parabolic distributed parameter systems. Commun. Nonlinear Sci. Numer. Simulat. 17(7), 2752–2765 (2012)
Vardakos, S., Gutierrez, M., Xia, C.C.: Parameter identification in numerical modeling of tunneling using the Differential Evolution Genetic Algorithm (DEGA). Tunnelling and Underground Space Technology 28, 109–123 (2012)
Qiu, Z.P., Wang, X.J.: Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach. International Journal of Solids and Structures 40(20), 5423–5439 (2003)
Wang, X.J., Qiu, Z.P.: Interval Algorithm for Membership-Set Identification of Linear Time-invariant System. Chinese Journal of Theoretical and Applied Mechanics 37(6), 713–718 (2005)
Wang, W.Z., Cai, J.S.: Optimal Algorithms of Set Member Identification for Parameters of MIMO Systems. Control Theroy and Applications 14(3), 402–406 (1997)
Yuan, Z.D., Xu, Q.N.: Set Membership Identification for the Parameters of MIMO System. Control Theory and Applications 11(4), 404–412 (1994)
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Wang, X., Yang, C., Zhang, B., Wang, L. (2013). Interval Algorithm for Set-Membership Identification of MIMO LTI System. In: Qin, Z., Huynh, VN. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2013. Lecture Notes in Computer Science(), vol 8032. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39515-4_11
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DOI: https://doi.org/10.1007/978-3-642-39515-4_11
Publisher Name: Springer, Berlin, Heidelberg
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