On recovering the parameters and velocity state of the Duffing's oscillator |
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| Affiliation: | 1. Department of Electrical Engineering and Electronics, Osaka Sangyo University, Nakagaito 3-1-1, Daito, Osaka 574-8530, Japan;2. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, PR China;3. Department of Mathematics, Hunan Normal University, Hunan, Changsha 410081, PR China;4. Graduate School of the Chinese Academy of Sciences, Beijing 100039, PR China;1. Laboratory of Nonlinear Modelling and Simulation in Engineering and Biological Physics, Faculty of Sciences, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon;2. Department of Physics, Faculty of Sciences, University of Douala, P.O. Box 24157, Douala, Cameroon;1. School of Science, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, PR China;2. College of Astronautics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, PR China;1. CIC-IPN, Av. Juan de Dios Bátiz s/n Esq. Manuel Othón de M. Unidad Profesional Adolfo López Mateos, Col. San Pedro Zacatenco, A.P. 75476, México, D.F. 07700, Mexico;2. CINVESTAV-IPN, Departamento de Control Automático, Av. IPN 2508, A.P. 14740, México, D.F. 07360, Mexico;1. Center for Nonlinear Science Studies, School of Science, Kunming University of Science and Technology, Kunming, Yunnan 650093, China;2. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China |
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| Abstract: | In this Letter, we propose a simple method to recover the unknown parameters and the velocity state from a known suitable output which is the position of the Duffing mechanical oscillator. We show that the system is constructible. Hence, it allows us to obtain an integral output parametrization of the remaining state. Based on this integral parametrization, we construct an iterative integral equation of the output. This method is numerically feasible and easy to implement by means of integrators, avoiding the necessity to evaluate the derivatives of the output. |
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