As for the drop of particle diversity and the slow convergent speed of particle in the late evolution period when particle swarm optimization（PSO） is applied to solve high-dimensional multi-modal functions,a hybrid ...As for the drop of particle diversity and the slow convergent speed of particle in the late evolution period when particle swarm optimization（PSO） is applied to solve high-dimensional multi-modal functions,a hybrid optimization algorithm based on the cat mapping,the cloud model and PSO is proposed.While the PSO algorithm evolves a certain of generations,this algorithm applies the cat mapping to implement global disturbance of the poorer individuals,and employs the cloud model to execute local search of the better individuals;accordingly,the obtained best individuals form a new swarm.For this new swarm,the evolution operation is maintained with the PSO algorithm,using the parameter of pop distr to balance the global and local search capacity of the algorithm,as well as,adopting the parameter of mix gen to control mixing times of the algorithm.The comparative analysis is carried out on the basis of 4 functions and other algorithms.It indicates that this algorithm shows faster convergent speed and better solving precision for solving functions particularly those high-dimensional multi-modal functions.Finally,the suggested values are proposed for parameters pop distr and mix gen applied to different dimension functions via the comparative analysis of parameters.展开更多
In order to prevent standard genetic algorithm (SGA) from being premature, chaos is introduced into GA, thus forming chaotic anneal genetic algorithm (CAGA). Chaos ergodicity is used to initialize the population, and ...In order to prevent standard genetic algorithm (SGA) from being premature, chaos is introduced into GA, thus forming chaotic anneal genetic algorithm (CAGA). Chaos ergodicity is used to initialize the population, and chaotic anneal mutation operator is used as the substitute for the mutation operator in SGA. CAGA is a unified framework of the existing chaotic mutation methods. To validate the proposed algorithm, three algorithms, i. e. Baum-Welch, SGA and CAGA, are compared on training hidden Markov model (HMM) to recognize the hand gestures. Experiments on twenty-six alphabetical gestures show the CAGA validity.展开更多
为进一步提高光伏发电功率超短期预测的准确度,提出一种基于混沌理论(Chaos)-集合经验模态分解(ensemble empirical mode decomposition,EEMD)-峰值频段划分(peak frequency band division,PFBD)和GA-BP神经网络的光伏发电功率组合预测...为进一步提高光伏发电功率超短期预测的准确度,提出一种基于混沌理论(Chaos)-集合经验模态分解(ensemble empirical mode decomposition,EEMD)-峰值频段划分(peak frequency band division,PFBD)和GA-BP神经网络的光伏发电功率组合预测法。首先,在光伏发电功率序列相空间重构的基础上,采用EEMD和PFBD对隐含混沌特征进行优化提取,以深度挖掘数据隐含波动信息,提取平稳性好、可预测性强的聚合分量;然后,利用GA优化BP神经网络(BPNN)的初始权值与阈值,构建GA-BP神经网络预测模型,进行光伏发电功率单步和三步预测;最后基于实测功率数据进行有效性验证。仿真结果表明:所提预测法通过数据分解重构和GA优化可实现预测准确度的提高,显示出良好预测性能。展开更多
The discovery of chaos in the sixties of last century was a breakthrough in concept,revealing the truth that some disorder behavior,called chaos,could happen even in a deterministic nonlinear system under barely deter...The discovery of chaos in the sixties of last century was a breakthrough in concept,revealing the truth that some disorder behavior,called chaos,could happen even in a deterministic nonlinear system under barely deterministic disturbance.After a series of serious studies,people begin to acknowledge that chaos is a specific type of steady state motion other than the conventional periodic and quasi-periodic ones,featuring a sensitive dependence on initial conditions,resulting from the intrinsic randomness of a nonlinear system itself.In fact,chaos is a collective phenomenon consisting of massive individual chaotic responses,corresponding to different initial conditions in phase space.Any two adjacent individual chaotic responses repel each other,thus causing not only the sensitive dependence on initial conditions but also the existence of at least one positive top Lyapunov exponent(TLE) for chaos.Meanwhile,all the sample responses share one common invariant set on the Poincaré map,called chaotic attractor,which every sample response visits from time to time ergodically.So far,the existence of at least one positive TLE is a commonly acknowledged remarkable feature of chaos.We know that there are various forms of uncertainties in the real world.In theoretical studies,people often use stochastic models to describe these uncertainties,such as random variables or random processes.Systems with random variables as their parameters or with random processes as their excitations are often called stochastic systems.No doubt,chaotic phenomena also exist in stochastic systems,which we call stochastic chaos to distinguish it from deterministic chaos in the deterministic system.Stochastic chaos reflects not only the intrinsic randomness of the nonlinear system but also the external random effects of the random parameter or the random excitation.Hence,stochastic chaos is also a collective massive phenomenon,corresponding not only to different initial conditions but also to different samples of the random parameter or the random excitation.Thus,the unique common feature of deterministic chaos and stochastic chaos is that they all have at least one positive top Lyapunov exponent for their chaotic motion.For analysis of random phenomena,one used to look for the PDFs(Probability Density Functions) of the ensemble random responses.However,it is a pity that PDF information is not favorable to studying repellency of the neighboring chaotic responses nor to calculating the related TLE,so we would rather study stochastic chaos through its sample responses.Moreover,since any sample of stochastic chaos is a deterministic one,we need not supplement any additional definition on stochastic chaos,just mentioning that every sample of stochastic chaos should be deterministic chaos.We are mainly concerned with the following two basic kinds of nonlinear stochastic systems,i.e.one with random variables as its parameters and one with ergodical random processes as its excitations.To solve the stochastic chaos problems of these two kinds of systems,we first transform the original stochastic system into their equivalent deterministic ones.Namely,we can transform the former stochastic system into an equivalent deterministic system in the sense of mean square approximation with respect to the random parameter space by the orthogonal polynomial approximation,and transform the latter one simply through replacing its ergodical random excitations by their representative deterministic samples.Having transformed the original stochastic chaos problem into the deterministic chaos problem of equivalent systems,we can use all the available effective methods for further chaos analysis.In this paper,we aim to review the state of art of studying stochastic chaos with its control and synchronization by the above-mentioned strategy.展开更多
In this paper, we discuss feedback control of a class of delay chaotic maps. Our aim is to drive the chaotic maps to its initially unstable fixed points by using linear and nonlinear state feedback control. The contro...In this paper, we discuss feedback control of a class of delay chaotic maps. Our aim is to drive the chaotic maps to its initially unstable fixed points by using linear and nonlinear state feedback control. The control is achieved by using small, bounded perturbations. Some numerical simulations are given to demonstrate the effectiveness of the proposed control method.展开更多
静态电压稳定性是一种理想化的稳定性概念,其扰动无限小的假设不利于强非线性的电力系统在静态电压稳定域(steady-state voltage stability region,SVSR)内的安全运行。针对功率大扰动场景下由SVSR内的边界危机所引发的吸引域骤缩问题,...静态电压稳定性是一种理想化的稳定性概念,其扰动无限小的假设不利于强非线性的电力系统在静态电压稳定域(steady-state voltage stability region,SVSR)内的安全运行。针对功率大扰动场景下由SVSR内的边界危机所引发的吸引域骤缩问题,提出了一种考虑边界危机的电压稳定域(voltage stability region considering boundary crises,BCVSR)的划分方法。首先通过流形分析研究了边界危机的发生机理及其对电压稳定性的影响。其次通过相轨迹分析验证了理论研究的结果。然后通过分岔分析研究了参数变化对直驱风电并网系统的平衡集及动态特性的影响。最后划分了系统在注入功率空间中的单参数与双参数BCVSR,并将其与SVSR进行了对比。研究结果表明,在考虑功率大扰动的情形下,BCVSR的划分排除了SVSR内的边界危机对系统电压稳定性的威胁,有助于指导电力系统在实际运行中的功率调整。展开更多
Nonlinear model predictive controllers(NMPC)can predict the future behavior of the under-controlled system using a nonlinear predictive model.Here,an array of hyper chaotic diagonal recurrent neural network(HCDRNN)was...Nonlinear model predictive controllers(NMPC)can predict the future behavior of the under-controlled system using a nonlinear predictive model.Here,an array of hyper chaotic diagonal recurrent neural network(HCDRNN)was proposed for modeling and predicting the behavior of the under-controller nonlinear system in a moving forward window.In order to improve the convergence of the parameters of the HCDRNN to improve system’s modeling,the extent of chaos is adjusted using a logistic map in the hidden layer.A novel NMPC based on the HCDRNN array(HCDRNN-NMPC)was proposed that the control signal with the help of an improved gradient descent method was obtained.The controller was used to control a continuous stirred tank reactor(CSTR)with hard-nonlinearities and input constraints,in the presence of uncertainties including external disturbance.The results of the simulations show the superior performance of the proposed method in trajectory tracking and disturbance rejection.Parameter convergence and neglectable prediction error of the neural network(NN),guaranteed stability and high tracking performance are the most significant advantages of the proposed scheme.展开更多
A class of map in which chaotic synchronization can occur is defined. The transverse Lyapunov exponents are used to determine the stability of synchronized trajectories. Some complex phenomena closely related to chaot...A class of map in which chaotic synchronization can occur is defined. The transverse Lyapunov exponents are used to determine the stability of synchronized trajectories. Some complex phenomena closely related to chaotic synchronization, namely riddled basin, riddling bifurcation and blowout bifurcation are theoretically analyzed. Riddling bifurcation and blowout bifurcation may change the synchronization stability of the system. And two types of riddled basins, i.e., global riddled basin and local riddled basin, may come into being after riddling bifurcation. An advertising competing model based on Vidale-Wolfe model is proposed and analyzed by the above theories at the end of the paper.展开更多
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education(20114307120032)the National Natural Science Foundation of China(71201167)
文摘As for the drop of particle diversity and the slow convergent speed of particle in the late evolution period when particle swarm optimization（PSO） is applied to solve high-dimensional multi-modal functions,a hybrid optimization algorithm based on the cat mapping,the cloud model and PSO is proposed.While the PSO algorithm evolves a certain of generations,this algorithm applies the cat mapping to implement global disturbance of the poorer individuals,and employs the cloud model to execute local search of the better individuals;accordingly,the obtained best individuals form a new swarm.For this new swarm,the evolution operation is maintained with the PSO algorithm,using the parameter of pop distr to balance the global and local search capacity of the algorithm,as well as,adopting the parameter of mix gen to control mixing times of the algorithm.The comparative analysis is carried out on the basis of 4 functions and other algorithms.It indicates that this algorithm shows faster convergent speed and better solving precision for solving functions particularly those high-dimensional multi-modal functions.Finally,the suggested values are proposed for parameters pop distr and mix gen applied to different dimension functions via the comparative analysis of parameters.
文摘In order to prevent standard genetic algorithm (SGA) from being premature, chaos is introduced into GA, thus forming chaotic anneal genetic algorithm (CAGA). Chaos ergodicity is used to initialize the population, and chaotic anneal mutation operator is used as the substitute for the mutation operator in SGA. CAGA is a unified framework of the existing chaotic mutation methods. To validate the proposed algorithm, three algorithms, i. e. Baum-Welch, SGA and CAGA, are compared on training hidden Markov model (HMM) to recognize the hand gestures. Experiments on twenty-six alphabetical gestures show the CAGA validity.
文摘为进一步提高光伏发电功率超短期预测的准确度,提出一种基于混沌理论(Chaos)-集合经验模态分解(ensemble empirical mode decomposition,EEMD)-峰值频段划分(peak frequency band division,PFBD)和GA-BP神经网络的光伏发电功率组合预测法。首先,在光伏发电功率序列相空间重构的基础上,采用EEMD和PFBD对隐含混沌特征进行优化提取,以深度挖掘数据隐含波动信息,提取平稳性好、可预测性强的聚合分量;然后,利用GA优化BP神经网络(BPNN)的初始权值与阈值,构建GA-BP神经网络预测模型,进行光伏发电功率单步和三步预测;最后基于实测功率数据进行有效性验证。仿真结果表明:所提预测法通过数据分解重构和GA优化可实现预测准确度的提高,显示出良好预测性能。
基金Project supported by National Natural Science Foundation of China (10872165)Northwestern Polytechnical University (CX200712)
文摘The discovery of chaos in the sixties of last century was a breakthrough in concept,revealing the truth that some disorder behavior,called chaos,could happen even in a deterministic nonlinear system under barely deterministic disturbance.After a series of serious studies,people begin to acknowledge that chaos is a specific type of steady state motion other than the conventional periodic and quasi-periodic ones,featuring a sensitive dependence on initial conditions,resulting from the intrinsic randomness of a nonlinear system itself.In fact,chaos is a collective phenomenon consisting of massive individual chaotic responses,corresponding to different initial conditions in phase space.Any two adjacent individual chaotic responses repel each other,thus causing not only the sensitive dependence on initial conditions but also the existence of at least one positive top Lyapunov exponent(TLE) for chaos.Meanwhile,all the sample responses share one common invariant set on the Poincaré map,called chaotic attractor,which every sample response visits from time to time ergodically.So far,the existence of at least one positive TLE is a commonly acknowledged remarkable feature of chaos.We know that there are various forms of uncertainties in the real world.In theoretical studies,people often use stochastic models to describe these uncertainties,such as random variables or random processes.Systems with random variables as their parameters or with random processes as their excitations are often called stochastic systems.No doubt,chaotic phenomena also exist in stochastic systems,which we call stochastic chaos to distinguish it from deterministic chaos in the deterministic system.Stochastic chaos reflects not only the intrinsic randomness of the nonlinear system but also the external random effects of the random parameter or the random excitation.Hence,stochastic chaos is also a collective massive phenomenon,corresponding not only to different initial conditions but also to different samples of the random parameter or the random excitation.Thus,the unique common feature of deterministic chaos and stochastic chaos is that they all have at least one positive top Lyapunov exponent for their chaotic motion.For analysis of random phenomena,one used to look for the PDFs(Probability Density Functions) of the ensemble random responses.However,it is a pity that PDF information is not favorable to studying repellency of the neighboring chaotic responses nor to calculating the related TLE,so we would rather study stochastic chaos through its sample responses.Moreover,since any sample of stochastic chaos is a deterministic one,we need not supplement any additional definition on stochastic chaos,just mentioning that every sample of stochastic chaos should be deterministic chaos.We are mainly concerned with the following two basic kinds of nonlinear stochastic systems,i.e.one with random variables as its parameters and one with ergodical random processes as its excitations.To solve the stochastic chaos problems of these two kinds of systems,we first transform the original stochastic system into their equivalent deterministic ones.Namely,we can transform the former stochastic system into an equivalent deterministic system in the sense of mean square approximation with respect to the random parameter space by the orthogonal polynomial approximation,and transform the latter one simply through replacing its ergodical random excitations by their representative deterministic samples.Having transformed the original stochastic chaos problem into the deterministic chaos problem of equivalent systems,we can use all the available effective methods for further chaos analysis.In this paper,we aim to review the state of art of studying stochastic chaos with its control and synchronization by the above-mentioned strategy.
基金the National Natural Science Foundation of China.
文摘In this paper, we discuss feedback control of a class of delay chaotic maps. Our aim is to drive the chaotic maps to its initially unstable fixed points by using linear and nonlinear state feedback control. The control is achieved by using small, bounded perturbations. Some numerical simulations are given to demonstrate the effectiveness of the proposed control method.
文摘静态电压稳定性是一种理想化的稳定性概念,其扰动无限小的假设不利于强非线性的电力系统在静态电压稳定域(steady-state voltage stability region,SVSR)内的安全运行。针对功率大扰动场景下由SVSR内的边界危机所引发的吸引域骤缩问题,提出了一种考虑边界危机的电压稳定域(voltage stability region considering boundary crises,BCVSR)的划分方法。首先通过流形分析研究了边界危机的发生机理及其对电压稳定性的影响。其次通过相轨迹分析验证了理论研究的结果。然后通过分岔分析研究了参数变化对直驱风电并网系统的平衡集及动态特性的影响。最后划分了系统在注入功率空间中的单参数与双参数BCVSR,并将其与SVSR进行了对比。研究结果表明,在考虑功率大扰动的情形下,BCVSR的划分排除了SVSR内的边界危机对系统电压稳定性的威胁,有助于指导电力系统在实际运行中的功率调整。
文摘Nonlinear model predictive controllers(NMPC)can predict the future behavior of the under-controlled system using a nonlinear predictive model.Here,an array of hyper chaotic diagonal recurrent neural network(HCDRNN)was proposed for modeling and predicting the behavior of the under-controller nonlinear system in a moving forward window.In order to improve the convergence of the parameters of the HCDRNN to improve system’s modeling,the extent of chaos is adjusted using a logistic map in the hidden layer.A novel NMPC based on the HCDRNN array(HCDRNN-NMPC)was proposed that the control signal with the help of an improved gradient descent method was obtained.The controller was used to control a continuous stirred tank reactor(CSTR)with hard-nonlinearities and input constraints,in the presence of uncertainties including external disturbance.The results of the simulations show the superior performance of the proposed method in trajectory tracking and disturbance rejection.Parameter convergence and neglectable prediction error of the neural network(NN),guaranteed stability and high tracking performance are the most significant advantages of the proposed scheme.
基金Supported by National Natural Science Foundation of P. R. China (60084003, 70171056)
文摘A class of map in which chaotic synchronization can occur is defined. The transverse Lyapunov exponents are used to determine the stability of synchronized trajectories. Some complex phenomena closely related to chaotic synchronization, namely riddled basin, riddling bifurcation and blowout bifurcation are theoretically analyzed. Riddling bifurcation and blowout bifurcation may change the synchronization stability of the system. And two types of riddled basins, i.e., global riddled basin and local riddled basin, may come into being after riddling bifurcation. An advertising competing model based on Vidale-Wolfe model is proposed and analyzed by the above theories at the end of the paper.
