Herein,a method of true-temperature inversion for a multi-wavelength pyrometer based on fractional-order particle-swarm optimization is proposed for difficult inversion problems with unknown emissivity.Fractional-order...Herein,a method of true-temperature inversion for a multi-wavelength pyrometer based on fractional-order particle-swarm optimization is proposed for difficult inversion problems with unknown emissivity.Fractional-order calculus has the inherent advantage of easily jumping out of local extreme values;here,it is introduced into the particle-swarm algorithm to invert the true temperature.An improved adaptive-adjustment mechanism is applied to automatically adjust the current velocity order of the particles and update their velocity and position values,increasing the accuracy of the true temperature values.The results of simulations using the proposed algorithm were compared with three algorithms using typical emissivity models:the internal penalty function algorithm,the optimization function(fmincon)algorithm,and the conventional particle-swarm optimization algorithm.The results show that the proposed algorithm has good accuracy for true-temperature inversion.Actual experimental results from a rocket-motor plume were used to demonstrate that the true-temperature inversion results of this algorithm are in good agreement with the theoretical true-temperature values.展开更多
Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has ...Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh–Rose(HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval(ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic(A-periodic)bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.展开更多
We investigate the quasi-synchronization of fractional-order complex networks(FCNs) with random coupling via quantized control. Firstly, based on the logarithmic quantizer theory and the Lyapunov stability theory, a n...We investigate the quasi-synchronization of fractional-order complex networks(FCNs) with random coupling via quantized control. Firstly, based on the logarithmic quantizer theory and the Lyapunov stability theory, a new quantized feedback controller, which can make all nodes of complex networks quasi-synchronization and eliminate the disturbance of random coupling in the system state, is designed under non-delay conditions. Secondly, we extend the theoretical results under non-delay conditions to time-varying delay conditions and design another form of quantization feedback controller to ensure that the network achieves quasi-synchronization. Furthermore, the error bound of quasi-synchronization is obtained.Finally, we verify the accuracy of our results using two numerical simulation examples.展开更多
A fractional-order cumulative optimization GM(1,2)model based on grey theory is proposed to study the relationship between torpedo loading and working reliabilities.In this model,the average relative error function re...A fractional-order cumulative optimization GM(1,2)model based on grey theory is proposed to study the relationship between torpedo loading and working reliabilities.In this model,the average relative error function related to order and background value is established.Taking the average relative error function as the objective function,the optimal value of the two parameters is obtained through the optimization method,and the minimum value of the average relative error is determined.The calculation example shows that this method can greatly improve the accuracy of the model and more accurately reflect the relationship between torpedo loading and working reliabilities compared with the traditional GM(1,2)model.展开更多
The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertaint...The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.展开更多
A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation i...A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback controller.Then,a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the controller.Finally,in order to verify the theoretical results,some numerical simulations are given.展开更多
A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strai...A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length.The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic time.Numerical calculations are performed to analyze the effects of the nonlocal strain gradient parameters,the spatiotemporal fractional order,the nonlocal characteristic length,and the memory characteristic time on the natural frequencies,the vibration attenuation,and the phase shift between the temperature field and the displacement field.The numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.展开更多
Although some numerical methods of the fractional-order chaotic systems have been announced,high-precision numerical methods have always been the direction that researchers strive to pursue.Based on this problem,this ...Although some numerical methods of the fractional-order chaotic systems have been announced,high-precision numerical methods have always been the direction that researchers strive to pursue.Based on this problem,this paper introduces a high-precision numerical approach.Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method.We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies.We investigate the influence of α_(1),α_(2),α_(3) on the numerical solution of fractional-order Lorenz chaotic systems.The simulation results of integer order are in good agreement with those of othermethods.The simulation results of numerical experiments demonstrate the effectiveness of the present method.展开更多
Purpose–This study aims to propose an adaptive fractional-order sliding mode controller to solve the problem of train speed tracking control and position interval control under disturbance environment in moving block...Purpose–This study aims to propose an adaptive fractional-order sliding mode controller to solve the problem of train speed tracking control and position interval control under disturbance environment in moving block system,so as to improve the tracking efficiency and collision avoidance performance.Design/methodology/approach–The mathematical model of information interaction between trains is established based on algebraic graph theory,so that the train can obtain the state information of adjacent trains,and then realize the distributed cooperative control of each train.In the controller design,the sliding mode control and fractional calculus are combined to avoid the discontinuous switching phenomenon,so as to suppress the chattering of sliding mode control,and a parameter adaptive law is constructed to approximate the time-varying operating resistance coefficient.Findings–The simulation results show that compared with proportional integral derivative(PID)control and ordinary sliding mode control,the control accuracy of the proposed algorithm in terms of speed is,respectively,improved by 25%and 75%.The error frequency and fluctuation range of the proposed algorithm are reduced in the position error control,the error value tends to 0,and the operation trend tends to be consistent.Therefore,the control method can improve the control accuracy of the system and prove that it has strong immunity.Originality/value–The algorithm can reduce the influence of external interference in the actual operating environment,realize efficient and stable tracking of trains,and ensure the safety of train control.展开更多
Classical thermo-viscoelastic models may be challenged to predict the precise thermo-mechanical behavior of viscoelastic materials without considering the memorydependent effect.Meanwhile,with the miniaturization of d...Classical thermo-viscoelastic models may be challenged to predict the precise thermo-mechanical behavior of viscoelastic materials without considering the memorydependent effect.Meanwhile,with the miniaturization of devices,the size-dependent effect on elastic deformation is becoming more and more important.To capture the memory-dependent effect and the size-dependent effect,the present study aims at developing a modified fractional-order thermo-viscoelastic coupling model at the microscale to account for two fundamentally distinct fractional-order models which govern the memory-dependent features of thermal conduction and stress-strain relation,respectively.Then,the modified theory is used to study the dynamic response of a polymer micro-rod heated by a moving heat source.The governing equations are obtained and solved by the Laplace transform method.In calculation,the effects of the fractional-order parameter,the fractional-order strain parameter,the mechanical relaxation parameter,and the nonlocal parameter on the variations of the considered variables are analyzed and discussed in detail.展开更多
In this paper, synchronization for a class of uncertain fractional-order neural networks with external disturbances is discussed by means of adaptive fuzzy control. Fuzzy logic systems, whose inputs are chosen as sync...In this paper, synchronization for a class of uncertain fractional-order neural networks with external disturbances is discussed by means of adaptive fuzzy control. Fuzzy logic systems, whose inputs are chosen as synchronization errors,are employed to approximate the unknown nonlinear functions. Based on the fractional Lyapunov stability criterion, an adaptive fuzzy synchronization controller is designed, and the stability of the closed-loop system, the convergence of the synchronization error, as well as the boundedness of all signals involved can be guaranteed. To update the fuzzy parameters,fractional-order adaptations laws are proposed. Just like the stability analysis in integer-order systems, a quadratic Lyapunov function is used in this paper. Finally, simulation examples are given to show the effectiveness of the proposed method.展开更多
The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is...The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is discrete and constant,which cannot affect the situation of the solution space and limit the diversity of bacterial population. In this paper, an improved QBFO(IQBFO) algorithm is proposed, which can adaptively make the quantum rotation angle continuously updated and enhance the global search ability. In the initialization process, the modified probability of the optimal rotation angle is introduced to avoid the existence of invariant solutions. The modified operator of probability amplitude is adopted to further increase the population diversity.The tests based on benchmark functions verify the effectiveness of the proposed algorithm. Moreover, compared with the integerorder PID controller, the fractional-order proportion integration differentiation(PID) controller increases the complexity of the system with better flexibility and robustness. Thus the fractional-order PID controller is applied to the servo system. The tuning results of PID parameters of the fractional-order servo system show that the proposed algorithm has a good performance in tuning the PID parameters of the fractional-order servo system.展开更多
It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well ...It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well as system’s parameters are concerned by treating the time delay and fractional order as additional parameters. The parameter estimation is converted into a multi-dimensional optimization problem. A new scheme based on artificial bee colony(ABC) algorithm is proposed to solve the optimization problem. Numerical experiments are performed on two typical time-delay fractional-order chaotic systems to verify the effectiveness of the proposed method.展开更多
In this paper,a new model identification method is developed for a class of delay fractional-order system based on the process step response.Four characteristic functions are defined to characterize the features of th...In this paper,a new model identification method is developed for a class of delay fractional-order system based on the process step response.Four characteristic functions are defined to characterize the features of the normalized fractionalorder model.Based on the time scaling technology,two identification schemes are proposed for parameters' estimation.The scheme one utilizes three exact points on the step response of the process to calculate model parameters directly.The other scheme employs optimal searching method to adjust the fractional order for the best model identification.The proposed two identification schemes are both applicable to any stable complex process,such as higher-order,under-damped/over-damped,and minimum-phase/nonminimum-phase processes.Furthermore,an optimal PID tuning method is proposed for the delay fractionalorder systems.The requirements on the stability margins and the negative feedback are cast as real part constraints(RPC)and imaginary part constraints(IPC).The constraints are implemented by trigonometric inequalities on the phase variable,and the optimal PID controller is obtained by the minimization of the integral of time absolute error(ITAE) index.Identification and control of a Titanium billet heating process is given for the illustration.展开更多
This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict...This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.展开更多
In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractio...In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay,the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.展开更多
Complex networks have attracted much attention from various fields of sciences and engineering in recent years.However, many complex networks have various uncertain information, such as unknown or uncertain system par...Complex networks have attracted much attention from various fields of sciences and engineering in recent years.However, many complex networks have various uncertain information, such as unknown or uncertain system parameters and topological structure, which greatly affects the system dynamics.Thus, the parameter estimation and structure identification problem has theoretical and practical importance for uncertain complex dynamical networks. This paper investigates identification of unknown system parameters and network topologies in uncertain fractional-order complex network with time delays(including coupling delay and node delay). Based on the stability theorem of fractional-order differential system and the adaptive control technique, a novel and general method is proposed to address this challenge. Finally two representative examples are given to verify the effectiveness of the proposed approach.展开更多
This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The frac...This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.展开更多
In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the intera...In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws,we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.展开更多
We present the joint probability density function(PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to ex...We present the joint probability density function(PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to examine the fractional-order moments of the bucket and the reference signals, in which the correlation orders are fractional numbers,other than positive integers in previous studies. The experimental results show that various images can be reconstructed from fractional-order moments. Negative(positive) ghost images are obtained with negative(positive) orders of the bucket signals. The visibility and peak signal-to-noise ratios of the diverse ghost images depend greatly on the fractional orders.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.62205280)the Graduate Innovation Foundation of Yantai University(Grant No.GGIFYTU2348).
文摘Herein,a method of true-temperature inversion for a multi-wavelength pyrometer based on fractional-order particle-swarm optimization is proposed for difficult inversion problems with unknown emissivity.Fractional-order calculus has the inherent advantage of easily jumping out of local extreme values;here,it is introduced into the particle-swarm algorithm to invert the true temperature.An improved adaptive-adjustment mechanism is applied to automatically adjust the current velocity order of the particles and update their velocity and position values,increasing the accuracy of the true temperature values.The results of simulations using the proposed algorithm were compared with three algorithms using typical emissivity models:the internal penalty function algorithm,the optimization function(fmincon)algorithm,and the conventional particle-swarm optimization algorithm.The results show that the proposed algorithm has good accuracy for true-temperature inversion.Actual experimental results from a rocket-motor plume were used to demonstrate that the true-temperature inversion results of this algorithm are in good agreement with the theoretical true-temperature values.
基金Project supported by the National Key Research and Development Program of China (Grant No.2018AAA0103300)the National Natural Science Foundation of China (Grant Nos.62171401 and 62071411)。
文摘Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh–Rose(HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval(ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic(A-periodic)bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.
基金supported by the Anhui Provincial Development and Reform Commission New Energy Vehicles and Intelligent Connected Automobile Industry Technology Innovation Project。
文摘We investigate the quasi-synchronization of fractional-order complex networks(FCNs) with random coupling via quantized control. Firstly, based on the logarithmic quantizer theory and the Lyapunov stability theory, a new quantized feedback controller, which can make all nodes of complex networks quasi-synchronization and eliminate the disturbance of random coupling in the system state, is designed under non-delay conditions. Secondly, we extend the theoretical results under non-delay conditions to time-varying delay conditions and design another form of quantization feedback controller to ensure that the network achieves quasi-synchronization. Furthermore, the error bound of quasi-synchronization is obtained.Finally, we verify the accuracy of our results using two numerical simulation examples.
文摘A fractional-order cumulative optimization GM(1,2)model based on grey theory is proposed to study the relationship between torpedo loading and working reliabilities.In this model,the average relative error function related to order and background value is established.Taking the average relative error function as the objective function,the optimal value of the two parameters is obtained through the optimization method,and the minimum value of the average relative error is determined.The calculation example shows that this method can greatly improve the accuracy of the model and more accurately reflect the relationship between torpedo loading and working reliabilities compared with the traditional GM(1,2)model.
基金supported by the Estonian Research Council(PRG658)。
文摘The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.
基金supported by the National Natural Science Foundation of China (U1703262,62163035,61866036,62006196,61963033,62163035)the Tianshan Innovation Team Program (2020D14017)the Tianshan Xuesong Program (2018XS02).
文摘A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback controller.Then,a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the controller.Finally,in order to verify the theoretical results,some numerical simulations are given.
基金the National Natural Science Foundation of China(Nos.12072022 and 11872105)the Fundamental Research Funds for the Central Universities(Nos.FRF-TW-2018-005 and FRF-BR-18-008B)。
文摘A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length.The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic time.Numerical calculations are performed to analyze the effects of the nonlocal strain gradient parameters,the spatiotemporal fractional order,the nonlocal characteristic length,and the memory characteristic time on the natural frequencies,the vibration attenuation,and the phase shift between the temperature field and the displacement field.The numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.
基金supported by the Natural Science Foundation of Inner Mongolia[2021MS01009]Jining Normal University[JSJY2021040,Jsbsjj1704,jsky202145].
文摘Although some numerical methods of the fractional-order chaotic systems have been announced,high-precision numerical methods have always been the direction that researchers strive to pursue.Based on this problem,this paper introduces a high-precision numerical approach.Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method.We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies.We investigate the influence of α_(1),α_(2),α_(3) on the numerical solution of fractional-order Lorenz chaotic systems.The simulation results of integer order are in good agreement with those of othermethods.The simulation results of numerical experiments demonstrate the effectiveness of the present method.
基金supported by the Natural Science Foundation of China under Grant 52162050R&D plan project for science and technology of China Railway(No.N2021G045).
文摘Purpose–This study aims to propose an adaptive fractional-order sliding mode controller to solve the problem of train speed tracking control and position interval control under disturbance environment in moving block system,so as to improve the tracking efficiency and collision avoidance performance.Design/methodology/approach–The mathematical model of information interaction between trains is established based on algebraic graph theory,so that the train can obtain the state information of adjacent trains,and then realize the distributed cooperative control of each train.In the controller design,the sliding mode control and fractional calculus are combined to avoid the discontinuous switching phenomenon,so as to suppress the chattering of sliding mode control,and a parameter adaptive law is constructed to approximate the time-varying operating resistance coefficient.Findings–The simulation results show that compared with proportional integral derivative(PID)control and ordinary sliding mode control,the control accuracy of the proposed algorithm in terms of speed is,respectively,improved by 25%and 75%.The error frequency and fluctuation range of the proposed algorithm are reduced in the position error control,the error value tends to 0,and the operation trend tends to be consistent.Therefore,the control method can improve the control accuracy of the system and prove that it has strong immunity.Originality/value–The algorithm can reduce the influence of external interference in the actual operating environment,realize efficient and stable tracking of trains,and ensure the safety of train control.
基金Project supported by the National Natural Science Foundation of China(Nos.11972176 and12062011)。
文摘Classical thermo-viscoelastic models may be challenged to predict the precise thermo-mechanical behavior of viscoelastic materials without considering the memorydependent effect.Meanwhile,with the miniaturization of devices,the size-dependent effect on elastic deformation is becoming more and more important.To capture the memory-dependent effect and the size-dependent effect,the present study aims at developing a modified fractional-order thermo-viscoelastic coupling model at the microscale to account for two fundamentally distinct fractional-order models which govern the memory-dependent features of thermal conduction and stress-strain relation,respectively.Then,the modified theory is used to study the dynamic response of a polymer micro-rod heated by a moving heat source.The governing equations are obtained and solved by the Laplace transform method.In calculation,the effects of the fractional-order parameter,the fractional-order strain parameter,the mechanical relaxation parameter,and the nonlocal parameter on the variations of the considered variables are analyzed and discussed in detail.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11401243 and 61403157)the Foundation for Distinguished Young Talents in Higher Education of Anhui Province,China(Grant No.GXYQZD2016257)+3 种基金the Fundamental Research Funds for the Central Universities of China(Grant No.GK201504002)the Natural Science Foundation for the Higher Education Institutions of Anhui Province of China(Grant Nos.KJ2015A256 and KJ2016A665)the Natural Science Foundation of Anhui Province,China(Grant No.1508085QA16)the Innovation Funds of Graduate Programs of Shaanxi Normal University,China(Grant No.2015CXB008)
文摘In this paper, synchronization for a class of uncertain fractional-order neural networks with external disturbances is discussed by means of adaptive fuzzy control. Fuzzy logic systems, whose inputs are chosen as synchronization errors,are employed to approximate the unknown nonlinear functions. Based on the fractional Lyapunov stability criterion, an adaptive fuzzy synchronization controller is designed, and the stability of the closed-loop system, the convergence of the synchronization error, as well as the boundedness of all signals involved can be guaranteed. To update the fuzzy parameters,fractional-order adaptations laws are proposed. Just like the stability analysis in integer-order systems, a quadratic Lyapunov function is used in this paper. Finally, simulation examples are given to show the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(6137415361473138)+2 种基金Natural Science Foundation of Jiangsu Province(BK20151130)Six Talent Peaks Project in Jiangsu Province(2015-DZXX-011)China Scholarship Council Fund(201606845005)
文摘The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is discrete and constant,which cannot affect the situation of the solution space and limit the diversity of bacterial population. In this paper, an improved QBFO(IQBFO) algorithm is proposed, which can adaptively make the quantum rotation angle continuously updated and enhance the global search ability. In the initialization process, the modified probability of the optimal rotation angle is introduced to avoid the existence of invariant solutions. The modified operator of probability amplitude is adopted to further increase the population diversity.The tests based on benchmark functions verify the effectiveness of the proposed algorithm. Moreover, compared with the integerorder PID controller, the fractional-order proportion integration differentiation(PID) controller increases the complexity of the system with better flexibility and robustness. Thus the fractional-order PID controller is applied to the servo system. The tuning results of PID parameters of the fractional-order servo system show that the proposed algorithm has a good performance in tuning the PID parameters of the fractional-order servo system.
基金supported by National Natural Science Foundation of China(11371049)
文摘It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well as system’s parameters are concerned by treating the time delay and fractional order as additional parameters. The parameter estimation is converted into a multi-dimensional optimization problem. A new scheme based on artificial bee colony(ABC) algorithm is proposed to solve the optimization problem. Numerical experiments are performed on two typical time-delay fractional-order chaotic systems to verify the effectiveness of the proposed method.
基金supported by National Natural Science Foundation of China(61403149,61573298)Natural Science Foundation of Fujian Province(2015J01261,2016J05165)Foundation of Huaqiao University(Z14Y0002)
文摘In this paper,a new model identification method is developed for a class of delay fractional-order system based on the process step response.Four characteristic functions are defined to characterize the features of the normalized fractionalorder model.Based on the time scaling technology,two identification schemes are proposed for parameters' estimation.The scheme one utilizes three exact points on the step response of the process to calculate model parameters directly.The other scheme employs optimal searching method to adjust the fractional order for the best model identification.The proposed two identification schemes are both applicable to any stable complex process,such as higher-order,under-damped/over-damped,and minimum-phase/nonminimum-phase processes.Furthermore,an optimal PID tuning method is proposed for the delay fractionalorder systems.The requirements on the stability margins and the negative feedback are cast as real part constraints(RPC)and imaginary part constraints(IPC).The constraints are implemented by trigonometric inequalities on the phase variable,and the optimal PID controller is obtained by the minimization of the integral of time absolute error(ITAE) index.Identification and control of a Titanium billet heating process is given for the illustration.
文摘This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.
基金supported by National Natural Science Foundation of China(61573194,61374180,61573096)China Postdoctoral Science Foundation Funded Project(2013M530229)+3 种基金China Postdoctoral Science Special Foundation Funded Project(2014T70463)Six Talent Peaks High Level Project of Jiangsu Province(ZNDW-004)Science Foundation of Nanjing University of Posts and Telecommunications(NY213095)Australian Research Council(DP120104986)
文摘In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay,the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.
基金supported by the Basic and Frontier Research Project of Chongqing(cstc2013jcyj A70006,cstc2015jcyj A40038)
文摘Complex networks have attracted much attention from various fields of sciences and engineering in recent years.However, many complex networks have various uncertain information, such as unknown or uncertain system parameters and topological structure, which greatly affects the system dynamics.Thus, the parameter estimation and structure identification problem has theoretical and practical importance for uncertain complex dynamical networks. This paper investigates identification of unknown system parameters and network topologies in uncertain fractional-order complex network with time delays(including coupling delay and node delay). Based on the stability theorem of fractional-order differential system and the adaptive control technique, a novel and general method is proposed to address this challenge. Finally two representative examples are given to verify the effectiveness of the proposed approach.
基金Project supported by the National Natural Science Foundation of China(Nos.11790282,U1534204,and 11472179)the Natural Science Foundation of Hebei Province of China(No.A2016210099)
文摘This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.
基金supported by the National Natural Science Foundation of China(61303211)Zhejiang Provincial Natural Science Foundation of China(LY17F030003,LY15F030009)
文摘In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws,we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674273,11304016,and 11204062)
文摘We present the joint probability density function(PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to examine the fractional-order moments of the bucket and the reference signals, in which the correlation orders are fractional numbers,other than positive integers in previous studies. The experimental results show that various images can be reconstructed from fractional-order moments. Negative(positive) ghost images are obtained with negative(positive) orders of the bucket signals. The visibility and peak signal-to-noise ratios of the diverse ghost images depend greatly on the fractional orders.
