---

Discontinuity, Nonlinearity, and Complexity 14(1) (2025) 1--9 | DOI:10.5890/DNC.2025.03.001

Jianzhe Huang, Binghang Xiao

School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China

Download Full Text PDF

 

Abstract

The dynamical model for a dynamical system might change during its full life cycle, and it is important to update the corresponding model during such a system is on duty. In this paper, a Filippov-type discontinuous dynamical system which is consisted with multiple sub-systems is investigated. The switching functions for such a discontinuous dynamical system switching from one sub-system to another, as well as the system parameters of the sub-systems are considered to be time-varying. When such a Filippov-type discontinuous dynamical system is governed by one of the sub-systems, the actual excitations including internal and external forces will be evaluated through super-twisting sliding mode observer and recursive least squares in case of inaccurate sub-system modeling and system parameters variation. The event-triggered technique will be adopted to identify the change of the switching functions, and a novel method to updating the switching functions will be designed. The generalized equations of such a self-updating approach will be provided for such a Filippov-type discontinuous dynamical model, which can be further extended to build the confidential digital twin model.

Acknowledgments

This work is partially supported by the 14th 5-years National Defense Pre-Research Foundation of China under Grant No. 50917060301, National Nature Science Foundation of China under Grant No. 11901385, National Science Foundation of Chongqing under Grant No. cstc2021jcyj-msxmX0089, the Fundamental Research Funds for the Central Universities.

References

1. [1]	Tao, F., Sui, F., Liu, A., Qi, Q., Zhang, M., Song, B., Guo, Z., Lu, S.C.Y., and Nee, A.Y.C. (2019), Digital twin-driven product design framework, International Journal of Production Research, 57(12), 3935-3953.

2. [2]	Rosen, R., Wichert, G.V., Lo, G., and Bettenhausen, K.D. (2015), About the importance of autonomy and digital twins for the future of manufacturing, IFAC-PapersOnLine, 48(3), 567-572.

3. [3]	Li, C., Mahadevan, S., Ling, Y., Choze, S., and Wang, L. (2017), Dynamic Bayesian network for aircraft wing health monitoring digital twin, AIAA Journal, 55(3), 930-941.

4. [4]	Tao, F., Zhang, H., Liu, A., and Nee, A.Y.C. (2019), Digital twin in industry: state-of-the-art, IEEE Transactions on Industrial Informatics, 15(4), 2405-2415.

5. [5]	Chavent, G. (1974), Identification of functional parameters in partial differential equations, 1974 Joint Automatic Control Conference, Austin, TX, June 17-21, 1974.

6. [6]	Chavent, G. (1974), Identification of distributed parameter systems: about the output least square method, its implementation, and identifiability, IFAC Proceedings Volumes, 12(8), 85-97.

7. [7]	Dee, D.P. (1995), On-line estimation of error covariance parameters for atmospheric data assimilation, Monthly Weather Review, 123, 1128-1145.

8. [8]	Evensen, G. and Fario, N. (1997), Solving for the generalized inverse of the Lorenz model, Journal of the Meteorological Society of Japan, 75(1B), 229-243.

9. [9]	Yang, X. and Delsole, T. (2009), Using the ensemble Karman filter to estimate multiplicative model parameters, Tellus, 61A, 601-609.

10. [10]	DelSole, T. and Yang, X. (2010), State and parameter estimation in stochastic dynamical models, Physica D, 239, 1781-1788.

11. [11]	Mehrkanoon, S., Falck, T., and Suykens, J.A.K. (2012), Parameter estimation for time varying dynamical systems using least squares support vector machines, IFAC Proceedings Volumes, 45(16), 1300-1305.

12. [12]	Abdessalem, A.B., Dervilis, N., Wagg, D., and Worden, K. (2019), Model selection and parameter estimation of dynamical systems using a novel variant of approximate Bayesian computation, Mechanical Systems and Signal Processing, 122, 364-386.

13. [13]	Ma, R., Ding, L., Liu, K., and Wu, H. (2019), Dynamical model identification for a small-scale unmanned helicopter using an integrated approach, International Journal of Aerospace Engineering, 2019, 8407013.

14. [14]	Li, C., Huang, Z., Huang, Z., Wang, Y., and Jiang, H. (2023), Digital twins in engineering dynamics: variational equation identification, feedback control design and their rapid update, Nonlinear Dynamics, 111(5), 4485-4500.

15. [15]	Levant, A. (2002), Construction principles of output-feedback 2-sliding mode design, the 41st IEEE Conference on Decision and Control, Las Vegas, NV, December 10-13, 2002.