© The Institution of Engineering and Technology
In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is introduced. Instead of relying on a Bayesian framework to include assumptions about the system in the definition of the covariance matrix of the parameters, here the prior knowledge is injected at the cost function level. The key idea is to define the regularisation matrix as a filtering operation on the parameters, which allows for a more intuitive formulation of the problem from an engineering point of view. Moreover, this results in a unified framework to model low-pass, band-pass and high-pass systems, and systems with one or more resonances. The proposed filter-based approach outperforms the existing regularisation method based on the TC and DC kernels, as illustrated by means of Monte Carlo simulations on several linear modelling examples.
References
-
-
1)
-
1. Ljung, L.: ‘System identification: theory for the user’ (Prentice-Hall, New Jersey, 1999, 2nd edn.).
-
2)
-
14. Chen, T., Ardeshiri, T., Carli, F., et al: ‘Maximum entropy properties of discrete-time first-order stable spline kernel’, Automatica, 2016, 66, pp. 34–38.
-
3)
-
4. Chen, T., Ohlsson, H., Ljung, L.: ‘On the estimation of transfer functions, regularizations and Gaussian processes - revisited’, Automatica, 2012, 48, (8), pp. 1525–1535.
-
4)
-
2. Pintelon, R., Schoukens, J.: ‘System identification: a frequency domain approach’ (Wiley-IEEE Press, 2012, 2nd edn.).
-
5)
-
8. Chen, T., Ljung, L.: ‘Regularized system identification using orthonormal basis functions’. 14th European Control Conf. (ECC'15), 2015.
-
6)
-
5. Rasmussen, C., Williams, C.: ‘Gaussian processes for machine learning’ (The MIT Press, 2006).
-
7)
-
10. Marconato, A., Schoukens, M., Schoukens, J.: ‘Filter interpretation of regularized impulse response modeling’. 15th European Control Conf. (ECC'16), Aalborg, Denmark, 2016.
-
8)
-
6. Pillonetto, G., Dinuzzo, F., Chen, T., et al: ‘Kernel methods in system identification, machine learning and function estimation: a survey’, Automatica, 2014, 50, (3), pp. 657–682.
-
9)
-
11. Chen, T., Ljung, L.: ‘Implementation of algorithms for tuning parameters in regularized least squares problems in system identification’, Automatica, 2013, 49, (7), pp. 2213–2220.
-
10)
-
12. Golub, G., Van Loan, C.: ‘Matrix computations’ (The Johns Hopkins University Press, 1996, 3rd edn.).
-
11)
-
13. Van Loan, C.: ‘Introduction to scientific computing’ (Prentice-Hall, 2000, 2nd edn.).
-
12)
-
9. Pillonetto, G., Chiuso, A., De Nicolao, G.: ‘Prediction error identification of linear systems: a nonparametric Gaussian regression approach’, Automatica, 2011, 47, pp. 291–305.
-
13)
-
3. Pillonetto, G., De Nicolao, G.: ‘A new kernel-based approach for linear system identification’, Automatica, 2010, 46, (1), pp. 81–93.
-
14)
-
16. Hastie, T., Tibshirani, R., Friedman, J.: ‘The elements of statistical learning: data mining, inference, and prediction’ (Springer-Verlag, 2009).
-
15)
-
17. Ljung, L.: ‘The system identification toolbox: the manual’ (The MathWorks Inc., Natick, MA, USA, 2013), Edition 8.3 2013.
-
16)
-
7. Chen, T., Ljung, L.: ‘Constructive state space model induced kernels for regularized system identification’. 19th IFAC World Congress, Cape Town, South Africa, 2014.
-
17)
-
15. Carli, F., Chen, T., Ljung, L.: ‘Maximum entropy kernels for system identification’, IEEE Trans. Automatic Control, 2016, .
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