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Closed-loop subspace-based identification algorithm using third-order cumulants. (English) Zbl 1167.93406

Summary: The problem of closed-loop system identification for coloured noise system without any knowledge of feedback controller is considered. We develop a solution to this problem in the framework of subspace identification based on high-order cumulants. The key of the developed algorithm is using the properties that the third-order cumulants are insensitive to any coloured Gaussian noises. By post-multiplying a suitable instrumental variable to the noise terms, the cross third-order cumulants are constructed that become zero when the noises are Gaussian distributed, and meanwhile the column rank of extended observability matrix is maintained. Thus, the standard subspace identification algorithms can be extended to closed-loop system corrupted by arbitrary coloured noises. A numerical simulation is presented to demonstrate the proposed algorithm.

MSC:

93E12 Identification in stochastic control theory
93E03 Stochastic systems in control theory (general)
93A30 Mathematical modelling of systems (MSC2010)
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[1] DOI: 10.1016/S0005-1098(99)00174-0 · Zbl 0984.93014 · doi:10.1016/S0005-1098(99)00174-0
[2] Brillinger DR, Time Series: Date Analysis and Theory (1981)
[3] DOI: 10.1016/S0005-1098(97)00092-7 · Zbl 0889.93011 · doi:10.1016/S0005-1098(97)00092-7
[4] DOI: 10.1109/78.902114 · doi:10.1109/78.902114
[5] DOI: 10.1109/78.224249 · Zbl 0825.93936 · doi:10.1109/78.224249
[6] DOI: 10.1109/9.384222 · Zbl 0824.93064 · doi:10.1109/9.384222
[7] DOI: 10.1109/9.29415 · Zbl 0687.93073 · doi:10.1109/9.29415
[8] DOI: 10.1109/78.740137 · doi:10.1109/78.740137
[9] DOI: 10.1016/0165-1684(96)00048-5 · Zbl 0875.94072 · doi:10.1016/0165-1684(96)00048-5
[10] DOI: 10.1109/TSP.2003.811232 · Zbl 1369.94206 · doi:10.1109/TSP.2003.811232
[11] Ljung L, System Identification: Theory for the Use (1999)
[12] DOI: 10.1109/9.508900 · Zbl 0855.93020 · doi:10.1109/9.508900
[13] Michael, CO, Lithgow, BJ and Robert, M. 2002. Speech features found in a continuous high order statistics analysis of speech. Proceedings of the 2nd Joint EMBS/EMES Conference. 2002, Houston, TX, USA. pp.180–181.
[14] DOI: 10.1109/78.285653 · doi:10.1109/78.285653
[15] DOI: 10.1016/0165-1684(96)00086-2 · doi:10.1016/0165-1684(96)00086-2
[16] Tugnait, JK and Zhou, Y. 1998. On closed-loop system identification using polyspectral analysis. Proceedings of the 37th IEEE Conference on Decision and Control. 1998, Tampa, Florida, USA. pp.3417–3422.
[17] DOI: 10.1016/0005-1098(95)00072-0 · Zbl 0849.93017 · doi:10.1016/0005-1098(95)00072-0
[18] Overschee, PVan and Moor, BDe. 1997. Close loop subspace system identification. Proceedings of 36th IEEE Conference on Decision and Control. 1997, SanDiego, USA. pp.1848–1853.
[19] DOI: 10.1016/0005-1098(93)90104-2 · Zbl 0850.93173 · doi:10.1016/0005-1098(93)90104-2
[20] Zhou, Y and Tugnait, JK. 1999. ”Subspace-based closed-loop system identification using polyspecctral analysis”. Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics. 1999. pp.62–65.
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