Model-Free Distributed Control of Dynamical Systems
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32870
Model-Free Distributed Control of Dynamical Systems

Authors: Javad Khazaei, Rick S. Blum

Abstract:

Distributed control is an efficient and flexible approach for coordination of multi-agent systems. One of the main challenges in designing a distributed controller is identifying the governing dynamics of the dynamical systems. Data-driven system identification is currently undergoing a revolution. With the availability of high-fidelity measurements and historical data, model-free identification of dynamical systems can facilitate the control design without tedious modeling of high-dimensional and/or nonlinear systems. This paper develops a distributed control design using consensus theory for linear and nonlinear dynamical systems using sparse identification of system dynamics. Compared with existing consensus designs that heavily rely on knowing the detailed system dynamics, the proposed model-free design can accurately capture the dynamics of the system with available measurements and input data and provide guaranteed performance in consensus and tracking problems. Heterogeneous damped oscillators are chosen as examples of dynamical system for validation purposes.

Keywords: Consensus tracking, distributed control, model-free control, sparse identification of dynamical systems.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 478

References:


[1] M. Liu, L. Tan, and S. Cao, “Method of dynamic mode decomposition and reconstruction with application to a three-stage multiphase pump,” Energy, vol. 208, p. 118343, 2020.
[2] H. Lu and D. M. Tartakovsky, “Prediction accuracy of dynamic mode decomposition,” SIAM Journal on Scientific Computing, vol. 42, no. 3, pp. A1639–A1662, 2020.
[3] C. Folkestad, D. Pastor, I. Mezic, R. Mohr, M. Fonoberova, and J. Burdick, “Extended dynamic mode decomposition with learned koopman eigenfunctions for prediction and control,” in 2020 american control conference (acc). IEEE, 2020, pp. 3906–3913.
[4] M. Al-Gabalawy, “Deep learning for koopman operator optimal control,” ISA transactions, 2021.
[5] A. Mauroy, I. Mezi´c, and Y. Susuki, The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications. Springer Nature, 2020, vol. 484.
[6] M. Schmidt and H. Lipson, “Distilling free-form natural laws from experimental data,” science, vol. 324, no. 5923, pp. 81–85, 2009.
[7] S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Discovering governing equations from data by sparse identification of nonlinear dynamical systems,” Proceedings of the national academy of sciences, vol. 113, no. 15, pp. 3932–3937, 2016.
[8] ——, “Sparse identification of nonlinear dynamics with control (sindyc),” IFAC-PapersOnLine, vol. 49, no. 18, pp. 710–715, 2016.
[9] E. Kaiser, J. N. Kutz, and S. L. Brunton, “Sparse identification of nonlinear dynamics for model predictive control in the low-data limit,” Proceedings of the Royal Society A, vol. 474, no. 2219, p. 20180335, 2018.
[10] D. Ding, Q.-L. Han, Z. Wang, and X. Ge, “A survey on model-based distributed control and filtering for industrial cyber-physical systems,” IEEE Transactions on Industrial Informatics, vol. 15, no. 5, pp. 2483–2499, 2019.
[11] A. Savitzky and M. J. Golay, “Smoothing and differentiation of data by simplified least squares procedures.” Analytical chemistry, vol. 36, no. 8, pp. 1627–1639, 1964.
[12] R. W. Schafer, “What is a savitzky-golay filter?
[lecture notes],” IEEE Signal Processing Magazine, vol. 28, no. 4, pp. 111–117, 2011.
[13] S. Larsson and V. Thom´ee, Partial differential equations with numerical methods. Springer, 2003, vol. 45.
[14] Z. Ding, “Consensus control of a class of nonlinear systems,” in 2013 9th Asian Control Conference (ASCC). IEEE, 2013, pp. 1–6.