References
- Aravkin, A. Y., Burke, J. V., & Pillonetto, G. (2018). Generalized system identification with stable spline kernels. SIAM Journal on Scientific Computing, 40(5), B1419–B1443. https://doi.org/https://doi.org/10.1137/16M1070517
- Baker, G. A., & Graves-Morris, P. (1996). Padé approximants (Vol. 59). Cambridge University Press.
- Bottegal, G., Risuleo, R. S., & Hjalmarsson, H. (2015). Blind system identification using kernel-based method. IFAC-PapersOnLine, 48(28), 466–471. 17th IFAC Symposium on System Identification SYSID 2015. https://doi.org/https://doi.org/10.1016/j.ifacol.2015.12.172
- Chen, T. (2018a). Continuous-time DC kernel – A stable generalized first-order spline kernel. IEEE Transactions on Automatic Control, 63(12), 4442–4447. https://doi.org/https://doi.org/10.1109/TAC.2018.2825365
- Chen, T. (2018b). On kernel design for regularized LTI system identification. Automatica, 90, 109–122. https://doi.org/https://doi.org/10.1016/j.automatica.2017.12.039
- Chen, F., Aguero, J. C., Gilson, M., Garnier, H., & Liu, T. (2017). EM-based identification of continuous-time ARMA models from irregularly sampled data. Automatica, 77, 293–301. https://doi.org/https://doi.org/10.1016/j.automatica.2016.11.020
- Chen, T., Ardeshiri, T., Carli, F. P., Chiuso, A., Ljung, L., & Pillonetto, G. (2016). Maximum entropy properties of discrete-time first-order stable spline kernel. Automatica, 66, 34–38. https://doi.org/https://doi.org/10.1016/j.automatica.2015.12.009
- Chen, F., Garnier, H., & Gilson, M. (2015). Robust identification of continuous-time models with arbitrary time-delay from irregularly sampled data. Journal of Process Control, 25, 19–27. https://doi.org/https://doi.org/10.1016/j.jprocont.2014.10.003
- Chen, T., Ohlsson, H., & Ljung, L. (2012). On the estimation of transfer functions, regularizations and Gaussian processes – Revisited. Automatica, 48(8), 1525–1535. https://doi.org/https://doi.org/10.1016/j.automatica.2012.05.026
- Darwish, M. A. H., Cox, P. B., Proimadis, I., Pillonetto, G., & Tóth, R. (2018). Prediction-error identification of LPV systems: A nonparametric Gaussian regression approach. Automatica, 97, 92–103. https://doi.org/https://doi.org/10.1016/j.automatica.2018.07.032
- Dinuzzo, F. (2015). Kernels for linear time invariant system identification. SIAM Journal on Control and Optimization, 53(5), 3299–3317. https://doi.org/https://doi.org/10.1137/130920319
- Dinuzzo, F., & Schölkopf, B. (2012). The representer theorem for Hilbert spaces: A necessary and sufficient condition. In F. Pereira, C. J. C. Burges, L. Bottou, & K. Q. Weinberger (Eds.), Advances in neural information processing systems (Vol. 25, pp. 189–196). Curran.
- Formentin, S., Mazzoleni, M., Scandella, M., & Previdi, F. (2019). Nonlinear system identification via data augmentation. Systems & Control Letters, 128, 56–63. https://doi.org/https://doi.org/10.1016/j.sysconle.2019.04.004
- Garnier, H. (2015). Direct continuous-time approaches to system identification. Overview and benefits for practical applications. European Journal of Control, 24, 50–62. SI: ECC15. https://doi.org/https://doi.org/10.1016/j.ejcon.2015.04.003
- Garnier, H., & Gilson, M. (2018). CONTSID: A Matlab toolbox for standard and advanced identification of black-box continuous-time models. IFAC-PapersOnLine, 51(15), 688–693. 18th IFAC Symposium on System Identification SYSID 2018. https://doi.org/https://doi.org/10.1016/j.ifacol.2018.09.203
- Garnier, H., & Wang, L. (2008). Identification of continuous-time models from sampled data. Springer.
- Garnier, H., & Young, P. C. (2012). What does continuous-time model identification have to offer? IFAC Proceedings Volumes, 45(16), 810–815. 16th IFAC Symposium on System Identification. https://doi.org/https://doi.org/10.3182/20120711-3-BE-2027.00233
- Golabi, A., Meskin, N., Toth, R., & Mohammadpour, J. (2017). A Bayesian approach for LPV model identification and its application to complex processes. IEEE Transactions on Control Systems Technology, 25(6), 2160–2167. https://doi.org/https://doi.org/10.1109/TCST.2016.2642159
- Lataire, J., Pintelon, R., Piga, D., & Tóth, R. (2017). Continuous-time linear time-varying system identification with a frequency-domain kernel-based estimator. IET Control Theory & Applications, 11(4), 457–465. https://doi.org/https://doi.org/10.1049/iet-cta.2016.0385
- Ljung, L., & Glad, T. (2016). Modeling & identification of dynamic systems. Studentlitteratur AB.
- Mazzoleni, M., Formentin, S., Scandella, M., & Previdi, F. (2018, June). Semi-supervised learning of dynamical systems: A preliminary study. In 2018 European control conference (ECC) (pp. 2824–2829). IEEE.
- Mazzoleni, M., Scandella, M., Formentin, S., & Previdi, F. (2018, December). Classification of light charged particles via learning-based system identification. In 2018 IEEE conference on decision and control (CDC) (pp. 6053–6058). IEEE.
- Mazzoleni, M., Scandella, M., & Previdi, F. (2019). A comparison of manifold regularization approaches for kernel-based system identification. Proceedings of the 13th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS-2019), Guildhall Winchester, Winchester, UK.
- Olver, F. W. J., Lozier, D. W., Boisvert, R. F., & Clark, C. W. (2010). Nist handbook of mathematical functions hardback and cd-rom. Cambridge University Press.
- Padilla, A., Garnier, H., Young, P. C., Chen, F., & Yuz, J. I. (2019). Identification of continuous-time models with slowly time-varying parameters. Control Engineering Practice, 93, 104165. https://doi.org/https://doi.org/10.1016/j.conengprac.2019.104165
- Paduart, J., Lauwers, L., Swevers, J., Smolders, K., Schoukens, J., & Pintelon, R. (2010). Identification of nonlinear systems using polynomial nonlinear state space models. Automatica, 46(4), 647–656. https://doi.org/https://doi.org/10.1016/j.automatica.2010.01.001
- Pascu, V., Garnier, H., Ljung, L., & Janot, A. (2019). Benchmark problems for continuous-time model identification: Design aspects, results and perspectives. Automatica, 107, 511–517. https://doi.org/https://doi.org/10.1016/j.automatica.2019.06.011
- Pillonetto, G. (2015, September). Identification of hybrid systems using stable spline kernels. In 2015 IEEE 25th international workshop on machine learning for signal processing (MLSP) (pp. 1–6).
- Pillonetto, G. (2018). System identification using kernel-based regularization: New insights on stability and consistency issues. Automatica, 93, 321–332. https://doi.org/https://doi.org/10.1016/j.automatica.2018.03.065
- Pillonetto, G., Carè, A., & Campi, M. C. (2018). Kernel-based SPS. IFAC-PapersOnLine, 51(15), 31–36. 18th IFAC Symposium on System Identification SYSID 2018. https://doi.org/https://doi.org/10.1016/j.ifacol.2018.09.086
- Pillonetto, G., Chiuso, A., & De Nicolao, G. (2019). Stable spline identification of linear systems under missing data. Automatica, 108, 108493. https://doi.org/https://doi.org/10.1016/j.automatica.2019.108493
- Pillonetto, G., & De Nicolao, G. (2010). A new kernel-based approach for linear system identification. Automatica, 46(1), 81–93. https://doi.org/https://doi.org/10.1016/j.automatica.2009.10.031
- Pillonetto, G., Dinuzzo, F., Chen, T., De Nicolao, G., & Ljung, L. (2014). Kernel methods in system identification, machine learning and function estimation: A survey. Automatica, 50(3), 657–682. https://doi.org/https://doi.org/10.1016/j.automatica.2014.01.001
- Pillonetto, G., Quang, M. H., & Chiuso, A. (2011). A new kernel-based approach for nonlinear system identification. IEEE Transactions on Automatic Control, 56(12), 2825–2840. https://doi.org/https://doi.org/10.1109/TAC.2011.2131830
- Pintelon, R., Guillaume, P., Rolain, Y., Schoukens, J., & Hamme, H. V. (1994). Parametric identification of transfer functions in the frequency domain-a survey. IEEE Transactions on Automatic Control, 39(11), 2245–2260. https://doi.org/https://doi.org/10.1109/9.333769
- Pintelon, R., & Schoukens, J. (2012). System identification. Wiley.
- Rao, G. P., & Garnier, H. (2002). Numerical illustrations of the relevance of direct continuous-time model indentification. IFAC Proceedings Volumes, 35(1), 133–138. 15th IFAC World Congress. https://doi.org/https://doi.org/10.3182/20020721-6-ES-1901.01008
- Risuleo, R. S., Bottegal, G., & Hjalmarsson, H. (2015, December). A new kernel-based approach to overparameterized Hammerstein system identification. In 2015 54th IEEE conference on decision and control (CDC) (pp. 115–120).
- Rudi, A., Camoriano, R., & Rosasco, L. (2015). Less is more: Nyström computational regularization. Advances in neural information processing systems (Vol. 28, pp. 1657–1665). Curran Associates, Inc.
- Rudi, A., Carratino, L., & Rosasco, L. (2017). Falkon: An optimal large scale kernel method. Advances in neural information processing systems (pp. 3888–3898). Curran Associates, Inc.
- Rüdinger, F., & Krenk, S. (2001). Non-parametric system identification from non-linear stochastic response. Probabilistic Engineering Mechanics, 16(3), 233–243. https://doi.org/https://doi.org/10.1016/S0266-8920(01)00005-4
- Scandella, M., Mazzoleni, M., Formentin, S., & Previdi, F. (2020). A note on the numerical solutions of kernel-based learning problems. IEEE Transactions on Automatic Control, 1. https://doi.org/https://doi.org/10.1109/TAC.9
- Schoukens, J., Pintelon, R., Vandersteen, G., & Guillaume, P. (1997). Frequency-domain system identification using non-parametric noise models estimated from a small number of data sets. Automatica, 33(6), 1073–1086. https://doi.org/https://doi.org/10.1016/S0005-1098(97)00002-2
- Shi, Z. Y., Law, S. S., & Xu, X. (2009). Identification of linear time-varying mdof dynamic systems from forced excitation using Hilbert transform and EMD method. Journal of Sound and Vibration, 321(3), 572–589. https://doi.org/https://doi.org/10.1016/j.jsv.2008.10.005
- Varga, A. (1991, December). Balancing free square-root algorithm for computing singular perturbation approximations. In Proceedings of the 30th IEEE conference on decision and control (Vol. 2, pp. 1062–1065). IEEE.
- Velleman, P. F., & Hoaglin, D. C. (1981). Applications, basics, and computing of exploratory data analysis. Duxbury Press.
- Wahba, G. (1990). Spline models for observational data. SIAM: Society for Industrial and Applied Mathematics.
- Wang, L., & Gawthrop, P. (2001). On the estimation of continuous time transfer functions. International Journal of Control, 74(9), 889–904. https://doi.org/https://doi.org/10.1080/00207170110037894
- Wellstead, P. E. (1981). Non-parametric methods of system identification. Automatica, 17(1), 55–69. https://doi.org/https://doi.org/10.1016/0005-1098(81)90084-4
- Young, P. C. (2011). Recursive estimation and time-series analysis. Springer.
- Young, P. C. (2015). Refined instrumental variable estimation: Maximum likelihood optimization of a unified Box–Jenkins model. Automatica, 52, 35–46. https://doi.org/https://doi.org/10.1016/j.automatica.2014.10.126