Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchroni...Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.展开更多
This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projectiv...This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.展开更多
Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（...Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986展开更多
In this paper, a square root cubature particle filter approach was designed to estimate the state of charge of lithium-ion battery,which not only enhanced the numerical stability and guaranteed positive definiteness o...In this paper, a square root cubature particle filter approach was designed to estimate the state of charge of lithium-ion battery,which not only enhanced the numerical stability and guaranteed positive definiteness of the state covariance, but also increased accuracy and decreased computation quantity. Due to the fractional characteristics of the battery capacitance, a fractional order model was used to formulate the lithium-ion battery. Considering the high accuracy and easy convergence, a particle swarm optimization algorithm was utilized to identify the model parameters. The above-mentioned approach was modelled and translated into C code, which was downloaded into battery control unit of battery management system for experimental validation. Two kinds of dynamic cycles were utilized to validate the proposed approach at different temperatures, where both unscent Kalman filter and cubature Kalman filter were compared with the proposed approach. Experimental results indicate that the proposed approach has better accuracy and robustness, and fractional order model is more accurate than integer order model.Therefore, the square root cubature particle filter with fractional order model of lithium-ion battery is a good candidate to estimate the state of charge.展开更多
Let c : SU(n) → PSU(n) = SU(n)/Zn be the quotient map of the special unitary group SU(n) by its center subgroup Z_n. We determine the induced homomorphism c*: H*(PSU(n)) → H*(SU(n)) on cohomologies by computing with...Let c : SU(n) → PSU(n) = SU(n)/Zn be the quotient map of the special unitary group SU(n) by its center subgroup Z_n. We determine the induced homomorphism c*: H*(PSU(n)) → H*(SU(n)) on cohomologies by computing with the prime orders of binomial coefficients.展开更多
基金supported by the Education Committee of Chongqing Province,China (Grant No.KJ090503)
文摘Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.
文摘This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.
文摘Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986
基金supported by the National Key Research and Development Program of China (Grant No. 2017YFB0103104)the Key Research and Development Program of Jiangsu Province (Grant No. BE2021006-2)the Innovation Project of New Energy Vehicle and Intelligent Connected Vehicle of Anhui Province,and the Foundation of State Key Laboratory of Automotive Simulation and Control (Grant No. 20201107)。
文摘In this paper, a square root cubature particle filter approach was designed to estimate the state of charge of lithium-ion battery,which not only enhanced the numerical stability and guaranteed positive definiteness of the state covariance, but also increased accuracy and decreased computation quantity. Due to the fractional characteristics of the battery capacitance, a fractional order model was used to formulate the lithium-ion battery. Considering the high accuracy and easy convergence, a particle swarm optimization algorithm was utilized to identify the model parameters. The above-mentioned approach was modelled and translated into C code, which was downloaded into battery control unit of battery management system for experimental validation. Two kinds of dynamic cycles were utilized to validate the proposed approach at different temperatures, where both unscent Kalman filter and cubature Kalman filter were compared with the proposed approach. Experimental results indicate that the proposed approach has better accuracy and robustness, and fractional order model is more accurate than integer order model.Therefore, the square root cubature particle filter with fractional order model of lithium-ion battery is a good candidate to estimate the state of charge.
基金supported by National Natural Science Foundation of China(Grant Nos.11131008,11401098 and 11661131004)National Basic Research Program of China(973 Program)(Grant No.2011CB302400)
文摘Let c : SU(n) → PSU(n) = SU(n)/Zn be the quotient map of the special unitary group SU(n) by its center subgroup Z_n. We determine the induced homomorphism c*: H*(PSU(n)) → H*(SU(n)) on cohomologies by computing with the prime orders of binomial coefficients.
