Skip to main content
Log in

Sparse parameter identification of stochastic dynamical systems

  • Letter
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

References

  1. Bonin, M., Seghezza, V., & Piroddi, L. (2010). LASSO-enhanced simulation error minimization method for NARX model selection. In Proceedings of the American control conference, (pp. 4522–4527) Baltimore, MD, USA.

  2. Chiuso, A., & Pillonetto, G. (2014). Bayesian and nonparametric methods for system identification and model selection. In Proceedings of the 13th European control conference (pp. 2376–2381). Strasbourg, France.

  3. Morici, S., Spiriti, E., & Piroddi, L. (2013). An indirect model selection algorithm for nonlinear active noise control. In Proceedings of the 12th European control conference (pp. 2910–2915). Zurich, Switzerland.

  4. Xiong, D., Chai, L., & Zhang, J. (2014). Sparse system identification using orthogonal rational functions. In Proceeding of the 11th World congress on intelligent control and automation (pp. 2340–2345). Shenyang, China.

  5. Candes, E., & Tao, T. (2006). Near optimal signal recovery from random projections: Universal encoding strategies? IEEE Transactions on Information Theory, 52(12), 5406–5425.

    Article  MathSciNet  Google Scholar 

  6. Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323–2326.

    Article  Google Scholar 

  7. Knight, K., & Fu, W. (2000). Asymptotics for Lasso-type estimators. The Annals of Statistics, 28, 1356–1378.

    MathSciNet  MATH  Google Scholar 

  8. Zou, H. (2006). The adaptive Lasso and its oracle properties. Journal of the American Statistical Association, 101(476), 1418–1429.

    Article  MathSciNet  Google Scholar 

  9. Debruyne, M., Hubert, M., & Suykens, J. A. K. (2008). Model selection in kernel based regression using the influence function. Journal of Machine Learning Research, 9, 2377–2400.

    MathSciNet  MATH  Google Scholar 

  10. Ojeda, F., Falck, T., De Moor, B., & Suykens, J. A. K. (2010). Polynomial componentwise LS-SVM: fast variable selection using low rank updates. In Proceedings of the 2010 international joint conference on neural networks (pp. 1–7). Barcelona, Spain.

  11. Chen, H. F., & Guo, L. (1991). Identification and stochastic adaptive control. Boston: Birkhäuser.

  12. Ljung, L. (1987). System identification: theory for users. Englewood Cliffs: Prentice Hall.

  13. Perepu, S. K., & Tangirala, A. K. (2015). Identification of equation error models from small samples using compressed sensing techniques. IFAC-PapersOnline, 48(8), 795–800.

  14. Kopsinis, Y., Slavakis, K., & Theodoridis, S. (2010). Online sparse system identification and signal reconstruction using projections onto weighted \(L_1\) balls. IEEE Transactions on Signal Processing, 59(3), 936–952.

    Article  Google Scholar 

  15. Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306.

    Article  MathSciNet  Google Scholar 

  16. Marjanovic, G., & Solo, V. (2012). On \(l_q\) optimization and matrix completion. IEEE Transactions on Signal Processing, 60(11), 5714–5724.

    Article  MathSciNet  Google Scholar 

  17. Tóth, R., Sanandaji, B.M., Poolla, K., & Vincent, T.L. (2012). Compressive system identification in the linear time-invariant framework. In Proceedings of IEEE conference on decision and control and European control conference, (pp. 783–790). Orlando, FL, USA.

  18. Gu, Y., Jin, J., & Mei, S. (2009). \(l_0\) norm constraint LMS algorithm for sparse system identification. IEEE Signal Processing Letters, 16(9), 774–777.

    Article  Google Scholar 

  19. Kalouptsidis, N., Mileounis, G., Babadi, B., & Tarokh, V. (2011). Adaptive algorithms for sparse system identification. Signal Processing, 91(8), 1910–1919.

    Article  Google Scholar 

  20. Cai, J., Luo, J., Wang, S., & Yang, S. (2018). Feature selection in machine learning: A new perspective. Neurocomputing, 300, 70–79.

    Article  Google Scholar 

  21. Chen, J., Stern, M., Wainwright, M. J., & Jordan, M. I. (2018). Kernel feature selection via conditional covariance minimization. arxiv:1707.01164.

  22. Song, L., Smola, A., Gretton, A., Bedo, J., & Borgwardt, K. (2012). Feature selection via dependence maximization. Journal of Machine Learning Research, 13, 1393–1434.

    MathSciNet  MATH  Google Scholar 

  23. Feng, J. & Simon, N. (2019). Sparse-input neural networks for high-dimensional nonparametric regression and classification. arxiv:1711.07592.

  24. Lemhadri, I., Ruan, F., Abraham, L., & Tibshirani, R. (2021). Lassonet: A neural network with feature sparsity. arxiv:1907.12207

  25. Lei, Q., Yen, I. E., Wu, C., Dhillon, I. S., & Ravikumar, P. (2017). Doubly greedy primal-dual coordinate descent for sparse empirical risk minimization. In Proceedings of the 34th International conference on machine learning (pp. 2034–2042). Sydney, Australia.

  26. Koltchinskii, V. (2009). Sparsity in penalized empirical risk minimization. Annales de l’Institut Henri Poincar, Probabilits et Statistiques, 45(1), 7–57.

    MathSciNet  MATH  Google Scholar 

  27. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso: a retrospective. Journal of the Royal Statistical Society, Series B: Methodological, 73, 273–282.

    Article  MathSciNet  Google Scholar 

  28. Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004). Least angle regression. The Annals of Statistics, 32, 407–499.

    Article  MathSciNet  Google Scholar 

  29. Pillonetto, G., Chen, T., & Ljung, L. (2013). Kernel-based model order selection for identification and prediction of linear dynamic systems. In Proceedings of the 52nd IEEE conference on decision and control (pp. 5174–5179). Florence, Italy.

  30. Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15), 3932–3937.

    Article  MathSciNet  Google Scholar 

  31. Simon, N., Friedman, J., Hastie, T., & Tibshirani, R. (2013). A sparse-group lasso. Journal of Computational and Graphical Statistics, 22(2), 231–245.

    Article  MathSciNet  Google Scholar 

  32. Peng, H., Long, F., & Ding, C. (2005). Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(8), 1226–1238.

    Article  Google Scholar 

  33. Tuv, E., Borisov, A., Runger, G., & Torkkola, K. (2009). Feature selection with ensembles, artificial variables, and redundancy elimination. Journal of Machine Learning Research, 10, 1341–1366.

    MathSciNet  MATH  Google Scholar 

  34. Yamada, M., Jitkrittum, W., Sigal, L., Xing, E. P., & Sugiyama, M. (2014). High-dimensional feature selection by feature-wise kernelized lasso. Neural Computation, 26(1), 185–207.

    Article  MathSciNet  Google Scholar 

  35. Cheng, C., & Bai, E. (2021). Variable selection based on squared derivative averages. Automatica, 127, 109491.

    Article  MathSciNet  Google Scholar 

  36. Zhao, W., Yin, G., & Bai, E. (2020). Sparse system identification for stochastic systems with general observation sequences. Automatica, 121, 109162.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wenxiao Zhao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, W. Sparse parameter identification of stochastic dynamical systems. Control Theory Technol. 20, 139–141 (2022). https://doi.org/10.1007/s11768-021-00077-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-021-00077-5

Navigation