The present paper develops two iterative algorithms to determine the periods and then the periodic solutions of nonlinear jerk equations. We consider two possible cases: initial values unknown and initial values given...
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The present paper develops two iterative algorithms to determine the periods and then the periodic solutions of nonlinear jerk equations. We consider two possible cases: initial values unknown and initial values given. A shape function method is introduced, by which we can transform the periodic problem to an initial value problem for the new variable, while the period and the terminal values of the new variable at the end of a period are determined iteratively. The initial value problem method (IVPM) can satisfy the periodic conditions exactly. Three examples reveal the advantages of the new iterative algorithms based on the IVPM, which converge fastly and also provide very accurate periodic solutions and periods of the nonlinear jerk equations. (C) 2019 Elsevier Ltd. All rights reserved.
In this paper, a novel iterative algorithm is developed for solving the coupled algebraic Riccati equation arising from the quadratic optimal control problem for continuous-time Markovian jump linear systems. First, t...
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In this paper, a novel iterative algorithm is developed for solving the coupled algebraic Riccati equation arising from the quadratic optimal control problem for continuous-time Markovian jump linear systems. First, two existing iterative algorithms to solve the coupled Riccati matrix equation are reviewed. Next, based on analysis for these two algorithms, a new iterative algorithm that combines both the information in the current iterative step and the information in the last iterative step is proposed. It is shown that the proposed algorithm with proper initial conditions can monotonically converge to the unique positive definite solution of the coupled Riccati matrix equation if the associated Markovian jump system is stochastically stabilizable. Also, numerical examples show that the presented algorithm is faster than some previous algorithms when the weighted parameter is appropriately selected. (C) 2019 Elsevier Inc. All rights reserved.
This paper proposes a new effective pseudo-spectral approximation to solve the Sylvester and Lyapunov matrix differential equations. The properties of the Chebyshev basis operational matrix of derivative are applied t...
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This paper proposes a new effective pseudo-spectral approximation to solve the Sylvester and Lyapunov matrix differential equations. The properties of the Chebyshev basis operational matrix of derivative are applied to convert the main equation to the matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained equations. Also, the error analysis of the propounded method is presented, which reveals the spectral rate of convergence. To illustrate the effectiveness of the proposed framework, several numerical examples are given.
In this work, we present an iterative algorithm to solve a class of generalized coupled Sylvester-conjugate matrix equations over the generalized Hamiltonian matrices. We show that if the equations are consistent, a g...
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In this work, we present an iterative algorithm to solve a class of generalized coupled Sylvester-conjugate matrix equations over the generalized Hamiltonian matrices. We show that if the equations are consistent, a generalized Hamiltonian solution can be obtained within finite iteration steps in the absence of round-offerrors for any initial generalized Hamiltonian matrix by the proposed iterative algorithm. Furthermore, we can obtain the minimum-norm generalized Hamiltonian solution by choosing the special initial matrices. Finally, numerical examples show that the iterative algorithm is effective. (C) 2021 Elsevier Inc. All rights reserved.
It is known that supercapacitors exhibits a voltage-dependent capacitance and the capacitance varies approximately linearly with voltage in the normal operation voltage range. To solve the online supercapacitor capaci...
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ISBN:
(纸本)9781728143231;9781728143224
It is known that supercapacitors exhibits a voltage-dependent capacitance and the capacitance varies approximately linearly with voltage in the normal operation voltage range. To solve the online supercapacitor capacity identification problem, which is an important function to implement in supercapacitor management system, firstly, linear least squares (LLS) is applied to get a closed-form solution based on a sequence of sampling terminal voltage and charging current data, and in the meanwhile, the details of voltage data processing to obtain more accurate differential capacitance values are elaborated. Secondly, to overcome the difficulty that the closed-form solution involves large data set, takes calculation of matrix inverse, and hence leads to heavy computing burden, an iterative algorithm of LLS is deduced, which gets rid of calculating matrix inverse directly, decomposes the computing burden of LLS into each sampling period, and therefore makes itself more applicable in online identification situations. Lastly, the effectiveness of the algorithm is verified by experiment.
We generate optimised phase masks by using an iterative Fourier Transform algorithm (IFTA) and use it for beam multiplexing in an experiment to generate an array of uniform spots in 1D and 2D. We quantify the efficacy...
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ISBN:
(纸本)9781510637795
We generate optimised phase masks by using an iterative Fourier Transform algorithm (IFTA) and use it for beam multiplexing in an experiment to generate an array of uniform spots in 1D and 2D. We quantify the efficacy of the iterative algorithm experimentally by computing the uniformity and the efficiency and show that the optimised phase masks yield multiplexed beamlets having high uniformity (similar to 90%). We also find that the algorithm converges within few tens of iterations requiring moderate computational budget and can be useful for almost real-time applications. We compare the performance of the iterative algorithm with global linear corrections in the look-up table (LUT) of a phase limited SLM and find that the former perform with about 20% better efficiency. Besides obtaining array of 1D/2D spots having high uniformity using IFTA, our result exemplifies the use of iterative algorithms for improving efficiency of phase limited SLMs, which is a less explored area of research.
This paper considers a problem of signal modeling for multi-frequency *** many characteristic parameters are contained in the multi-frequency signals,it is difficult to obtain these estimates of these characteristic *...
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This paper considers a problem of signal modeling for multi-frequency *** many characteristic parameters are contained in the multi-frequency signals,it is difficult to obtain these estimates of these characteristic *** to the different relations between the signal output and the amplitude parameters and frequency parameters of the multi-frequency sine signal,the signal parameters are divided into two parameter *** terms of these two different parameter sets,two identification sub-models are constructed for deriving two identification sub-algorithms by means of the gradient search and iterative *** uniting two identification algorithms,a joint gradient-based iterative signal modeling method is presented for estimating the total parameters of the multi-frequency sine *** performance of the proposed signal modeling method is validated through the computer simulations.
In this letter, we propose an iterative algorithm for the joint estimation of the channel covariance matrices and the channel vector for the spatially-correlated massive MIMO system with the following main advantages:...
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In this letter, we propose an iterative algorithm for the joint estimation of the channel covariance matrices and the channel vector for the spatially-correlated massive MIMO system with the following main advantages: low pilot overhead, improved mean square error (MSE), and low complexity. The results show that this scheme outperforms the conventional estimation schemes in terms of the required pilot overhead and the resulting MSE. The results also show that the achievable sum rate of the proposed scheme tends to that of the ideal case that the channel covariance matrices are assumed to be perfectly known at the base station.
Identifying the positive definiteness of an even-degree homogeneous polynomial form arises in various applications, such as evolutionary game dynamics, automatical control, magnetic resonance imaging, and spectral hyp...
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Identifying the positive definiteness of an even-degree homogeneous polynomial form arises in various applications, such as evolutionary game dynamics, automatical control, magnetic resonance imaging, and spectral hypergraph theory. However, it is difficult to determine whether a given homogeneous polynomial is positive definite or not because the problem is H-hard. In this paper, an iterative algorithm of identifying the positive definiteness of irreducible homogeneous polynomial forms is proposed by identifying strong H-tensors with weakly irreducibility. The validity of the iterative algorithm is proved theoretically. Experimental results on multilinear systems, high-order Markov chains and symmetric multi-player games are presented to illustrate the applications of the proposed methods. (C) 2019 Elsevier B.V. All rights reserved.
High-accuracy numerical method for uncertainty propagation analysis is a crucial issue in the field of structural reliability design. In this work, a novel iterative algorithm is proposed to study the free vibration o...
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High-accuracy numerical method for uncertainty propagation analysis is a crucial issue in the field of structural reliability design. In this work, a novel iterative algorithm is proposed to study the free vibration of the functionally graded (FG) thin plates with material uncertainties. As a highly accurate approach distinct from the existing non-iterative model, the frequency analysis of FG thin plates can be achieved by updating the lower and upper bounds of natural frequency step by step. Based on the classic plate theory, the governing equations of the FG thin plate resting on an elastic medium are derived and the analytical formulation for the natural frequency is presented. By introducing interval parameters to quantify the material uncertainties, a non-probabilistic model for evaluating the natural frequency response of the embedded FG thin plate is developed. Subsequently, the deduction of the novel iterative algorithm for solving the non-probabilistic model is given based on interval mathematics. The developed model and the proposed iterative algorithm are validated by the Monte Carlo method, and then the detailed parametric studies are carried out to explore the combined influences of material uncertainties, power-law index, and elastic foundation parameters, as well as size parameters on the natural frequency of the FG thin plate. Numerical results can provide useful guidance in the precise design of FG structures.
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