Rapid identification of switched systems: A data-driven method in variational framework
Source abstract
Abstract
Switched systems, i.e., systems changing the parameter values (even structural forms) abruptly and randomly at arbitrary instants, have been extensively utilized in many fields of modern industries. Rapid identification of switched systems, i.e., capturing all the changing instants and reconstructing the mathematical models rapidly, is of great significance for behavior prediction, performance evaluation and possible control, but is restricted by small data amount available. Here, the rapid identification problem is successfully solved by a data-driven method in variational framework. The data-driven method only requires a small amount of data due to the compact form of the variational description, and is robust to data noise due to the holistic viewpoint. Two numerical examples, i.e., Duffing oscillator and van der Pol system (as two representative systems in nonlinear dynamics), are adopted to illustrate its application, efficiency and robustness to noise.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Model Reduction and Neural Networks · Probabilistic and Robust Engineering Design · Control Systems and Identification
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (34)
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1. An J, Yan M, Zhou W, et al. Aircraft dynamic response to variable wing sweep geometry. J Aircraft, 1988, 25: 216–22110.2514/3.45580 ↗
2. Yan B, Li Y, Dai P, et al. Aerodynamic analysis, dynamic modeling, and control of a morphing aircraft. J Aerosp Eng, 2019, 32: 0401905810.1061/(ASCE)AS.1943-5525.0001047 ↗
3. Wang Y, Jin X, Huang Z. Stochastic averaging for quasi-integrable Hamiltonian systems with variable mass. J Appl Mech, 2014, 81: 05100310.1115/1.4025954 ↗
4. Cherniakov M. An Introduction to Parametric Digital Filters and Oscillators. Chichester: Wiley, 200310.1002/0470868252 ↗
5. Brunton S L, Kutz J N. Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control. Cambridge: Cambridge University Press, 201910.1017/9781108380690 ↗
6. Goodfellow I, Bengio Y, Courville A. Deep Learning. Cambridge: The MIT Press, 2016
7. Bishop CM. Pattern Recognition and Machine Learning. New York: Springer-Verlag, 2006
8. Chu S R, Shoureshi R, Tenorio M. Neural networks for system identification. IEEE Control Syst Mag, 1990, 10: 31–3510.1109/37.55121 ↗
9. Nelles O. Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models. New York: Springer-Verlag, 200110.1007/978-3-662-04323-3 ↗
10. Chen S, Billings S A, Grant P M. Non-linear system identification using neural networks. Int J Control, 1990, 51: 1191–121410.1080/00207179008934126 ↗
11. Kalman R E. A new approach to linear filtering and prediction problems. J Basic Eng, 1960, 82: 35–45a i]12_Juang J N, Pappa R S. An eigensystem realization algorithm for modal parameter identification and model reduction. J Guidance Control Dyn, 1985, 8: 620–62710.1115/1.3662552 ↗
12. Akaike H. Fitting autoregressive models for prediction. Ann Inst Stat Math, 1969, 21: 243–24710.1007/BF02532251 ↗
13. Bongard J, Lipson H. Automated reverse engineering of nonlinear dynamical systems. Proc Natl Acad Sci USA, 2007, 104: 9943–994810.1073/pnas.0609476104 ↗
14. Schmidt M, Lipson H. Distilling free-form natural laws from experimental data. Science, 2009, 324: 81–8510.1126/science.1165893 ↗
15. Quade M, Abel M, Shafi K, et al. Prediction of dynamical systems by symbolic regression. Phys Rev E, 2016, 94: 01221410.1103/PhysRevE.94.012214 ↗
16. Brunton S L, Proctor J L, Kutz J N. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc Natl Acad Sci USA, 2016, 113: 3932–393710.1073/pnas.1517384113 ↗
17. Wang W X, Yang R, Lai Y C, et al. Predicting catastrophes in nonlinear dynamical systems by compressive sensing. Phys Rev Lett, 2011, 106: 15410110.1103/PhysRevLett.106.154101 ↗
18. Schaeffer H, Tran G, Ward R. Learning dynamical systems and bifurcation via group sparsity..
19. Mangan N M, Kutz J N, Brunton S L, et al. Model selection for dynamical systems via sparse regression and information criteria. Proc R Soc A, 2017, 473: 2017000910.1098/rspa.2017.0009 ↗
20. Quade M, Abel M, Kutz J N, et al. Sparse identification ofnonlinear dynamics for rapid model recovery. Chaos, 2018, 28: 06311610.1063/1.5027470 ↗
21. Kaiser E, Kutz J N, Brunton S L. Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. Proc R Soc A, 2018, 474: 2018033510.1098/rspa.2018.0335 ↗
22. Huang Z, Tian Y, Li C, et al. Data-driven automated discovery of variational laws hidden in physical systems. J Mech Phys Solids, 2020, 137: 10387110.1016/j.jmps.2020.103871 ↗
23. Mukhopadhyay S C, Jayasundera K P, Postolache O A. Modern Sensing Technologies. Cham: Springer, 201910.1007/978-3-319-99540-3 ↗
24. Whittaker E T. A Treatise on the Analytical Dynamics of Particles and Rigid Bodies with an Introduction to the Problem of Three Bodies. London: Cambridge University Press, 1917
25. Lurie A I. Analytical Mechanics. Berlin: Springer-Verlag, 200210.1007/978-3-540-45677-3 ↗
26. Ben-Israel A, Greville T N E. Generalized Inverses: Theory and Applications. New York: Springer, 2003
27. Ott E. Chaos in Dynamical Systems. New York: Cambridge University Press, 200210.1017/CBO9780511803260 ↗
28. Schöll E, Schuster H G. Handbook of Chaos Control. Weinheim: Wiley-VCH, 200710.1002/9783527622313 ↗
29. Nayfeh A H, Mook D T. Nonlinear Oscillations. New York: John Wiley, 1979
30. Bhaskar R, Nigam A. Qualitative physics using dimensional analysis. Artificial Intell, 1990, 45: 73–11110.1016/0004-3702(90)90038-2 ↗
31. Lin Y K, Cai G Q. Probabilistic Structural Dynamics: Advanced Theory and Application. New York: McGraw-Hill. 1995
32. Camacho E F, Bordons C. Model Predictive Control in the Process Industry. London: Springer, 199510.1007/978-1-4471-3008-6 ↗
33. Grüne L, Pannek J. Nonlinear Model Predictive Control: Theory and Algorithms. London: Springer, 2016
34. Yang Y, Wang Y, Jin X, et al. Stochastic averaging-based direct method for response control of nonlinear vibrating system. J Eng Mech, 2019, 145: 0401901510.1061/(ASCE)EM.1943-7889.0001585 ↗