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Statistical Analysis of Block Coordinate Descent Algorithms for Linear Continuous-time System Identification (2404.09071v1)
Published 13 Apr 2024 in eess.SY and cs.SY
Abstract: Block coordinate descent is an optimization technique that is used for estimating multi-input single-output (MISO) continuous-time models, as well as single-input single output (SISO) models in additive form. Despite its widespread use in various optimization contexts, the statistical properties of block coordinate descent in continuous-time system identification have not been covered in the literature. The aim of this paper is to formally analyze the bias properties of the block coordinate descent approach for the identification of MISO and additive SISO systems. We characterize the asymptotic bias at each iteration, and provide sufficient conditions for the consistency of the estimator for each identification setting. The theoretical results are supported by simulation examples.
- Prentice-Hall, 1999.
- H. Garnier and L. Wang (Eds.), Identification of Continuous-time Models from Sampled Data. Springer, 2008.
- H. Garnier and P. C. Young, “The advantages of directly identifying continuous-time transfer function models in practical applications,” Int. J. of Control, vol. 87, no. 7, pp. 1319–1338, 2014.
- P. C. Young and A. J. Jakeman, “Refined instrumental variable methods of recursive time-series analysis. Part III, Extensions,” Int. J. of Control, vol. 31, no. 4, pp. 741–764, 1980.
- H. Garnier, M. Gilson, P. C. Young, and E. Huselstein, “An optimal IV technique for identifying continuous-time transfer function model of multiple input systems,” Control Eng. Pract., pp. 471–486, 2007.
- H. Kirchsteiger, S. Pölzer, R. Johansson, E. Renard, and L. del Re, “Direct continuous time system identification of MISO transfer function models applied to type 1 diabetes,” in 50th IEEE Conference on Decision and Control, pp. 5176–5181, 2011.
- F. Chen, P. C. Young, H. Garnier, Q. Deng, and M. K. Kazimierczuk, “Data-driven modeling of wireless power transfer systems with multiple transmitters,” IEEE Tran. on P. Electronics, vol. 35, no. 11, pp. 11363–11379, 2020.
- R. A. González, C. R. Rojas, S. Pan, and J. Welsh, “Parsimonious identification of continuous-time systems: A block-coordinate descent approach,” in 22nd IFAC World Congress (IFAC 2023), 2023.
- Springer, 2008.
- I. Necoara, Y. Nesterov, and F. Glineur, “Random block coordinate descent methods for linearly constrained optimization over networks,” J. of Opt. Theory and Applications, vol. 173, pp. 227–254, 2017.
- A. Quaglino, M. Gallieri, J. Masci, and J. Koutník, “SNODE: Spectral discretization of neural ODEs for system identification,” International Conference on Learning Representations, 2020.
- S. Pan, R. A. González, J. S. Welsh, and C. R. Rojas, “Consistency analysis of the Simplified Refined Instrumental Variable method for Continuous-time systems,” Automatica, vol. 113, Art. 108767, 2020.
- S. Pan, J. S. Welsh, R. A. González, and C. R. Rojas, “Efficiency analysis of the Simplified Refined Instrumental Variable method for Continuous-time systems,” Automatica, vol. 121, Art. 109196, 2020.
- P. C. Young, “Refined instrumental variable estimation: Maximum Likelihood optimization of a unified Box–Jenkins model,” Automatica, vol. 52, pp. 35–46, 2015.
- R. A. González, C. R. Rojas, S. Pan, and J. S. Welsh, “Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop,” Automatica (in Press).
- T. Söderström and P. Stoica, Instrumental Variable Methods for System Identification. Springer, 1983.
- Springer, 2012.
- T. Söderström, “Ergodicity results for sample covariances,” Problems of Control and Information Theory, vol. 4, no. 2, pp. 131–138, 1975.
- R. A. González, C. R. Rojas, S. Pan, and J. S. Welsh, “Consistent identification of continuous-time systems under multisine input signal excitation,” Automatica, vol. 133, Art. 109859, 2020.
- R. A. González, K. Classens, C. R. Rojas, J. Welsh, and T. Oomen, “Identification of additive continuous-time systems in open and closed-loop,” arXiv preprint arXiv:2401.01263, 2024.
- Rodrigo A. González (23 papers)
- Koen Classens (9 papers)
- Cristian R. Rojas (75 papers)
- James S. Welsh (19 papers)
- Tom Oomen (64 papers)