Parameter identification of conservative Hamiltonian systems using first integrals
Parameter identification of conservative Hamiltonian systems using first integrals
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DOI：
10.1016/j.amc.2019.124860
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发表时间：
2020-03
期刊：
影响因子：
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通讯作者：
Roger Miranda‐Colorado
中科院分区：
文献类型：
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作者：
Roger Miranda‐Colorado
本文提出了一种保守哈密顿系统非线性参数辨识的方法。在所提出的方法中，系统的哈密顿量下使用的第一积分的概念。利用该第一积分函数的时间导数来构造称为表面变量的信号，该表面变量取决于系统的参数。然后，通过将该表面变量向零驱动，采用参数估计作为控制输入来确保参数收敛。这一过程是接近处理的参数识别问题作为一个最优化问题。因此，不同的成本函数被定义，以获得不同的参数更新的法律。此外，提出了一种基于元启发式算法的自适应增益调整方法。所提出的方案表明，当表面变量达到零时，参数估计收敛到真实的。此外，当应用自动调谐方案时，获得更好的估计结果。大量的数值仿真验证了所提出的参数识别方法，包括未知系统变量估计通过脏导数和滑模微分器的情况下。
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.