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Parameter identification of conservative Hamiltonian systems using first integrals

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  • Miranda-Colorado, Roger

Abstract

This paper presents a methodology for nonlinear parameter identification of conservative Hamiltonian systems. In the proposed approach, the system’s Hamiltonian is used under the first integral concept. The time derivative of this first integral function is utilized to construct a signal termed surface variable, which depends on the system’s parameters. Then, the parameter convergence is ensured by driving this surface variable towards zero, employing the parameter estimates as control inputs. This procedure is approached by treating the parameter identification problem as an optimization one. Hence, different cost functions are defined to obtain various parameter updating laws. Besides, an automatic tuning methodology based on a meta-heuristic algorithm is proposed for tuning the adaptation gains of the new parameter updating laws. The proposed scheme shows that, when the surface variable reaches zero, the parameter estimates converge to the real ones. Furthermore, better estimation results are obtained when applying the automatic tuning scheme. Numerous numerical simulations validate the proposed parameter identification methodology, including the cases where the unknown system variables are estimated through the dirty derivative and a sliding-mode differentiator.

Suggested Citation

  • Miranda-Colorado, Roger, 2020. "Parameter identification of conservative Hamiltonian systems using first integrals," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308525
    DOI: 10.1016/j.amc.2019.124860
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    References listed on IDEAS

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    1. Zhou, Zhengxin, 2015. "On the first integral and equivalence of nonlinear differential equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 295-302.
    2. Fedele, Giuseppe & D’Alfonso, Luigi & Pin, Gilberto & Parisini, Thomas, 2018. "Volterra’s kernels-based finite-time parameters estimation of the Chua system," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 121-130.
    3. Liu, Xueying & Fu, Meiling, 2015. "Cuckoo search algorithm based on frog leaping local search and chaos theory," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1083-1092.
    4. Song, Chuan-Jing & Zhang, Yi, 2017. "Conserved quantities for Hamiltonian systems on time scales," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 24-36.
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