For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The propose...For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.展开更多
Timely detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meanings. We introduce a complexity measure for time series： the base-scale entropy. The definition d...Timely detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meanings. We introduce a complexity measure for time series： the base-scale entropy. The definition directly applies to arbitrary real-word data. We illustrate our method on a practical speech signal and in a theoretical chaotic system. The results show that the simple and easily calculated measure of base-scale entropy can be effectively used to detect qualitative and quantitative dynamical changes.展开更多
In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation ...In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.展开更多
This paper presents the work carried out to evaluate the dynamic performance of the Hybrid Variable Reluctance Motor (HVRM). The fourth-order Runge-Kutta integration algorithm was employed to solve the equations of th...This paper presents the work carried out to evaluate the dynamic performance of the Hybrid Variable Reluctance Motor (HVRM). The fourth-order Runge-Kutta integration algorithm was employed to solve the equations of the dynamic model, in conjunction with the three-dimensional finite element method. The 3D numerical data was calculated using Comsol Multiphysics, which accounts for the nonlinearity of the ferromagnetic material and the 3D nature of the HVRM. The outcomes of this study are precise and accurately predict the dynamic behaviour of the HVRM in terms of rotor position response, rotational speed and torque. The distinctive contribution of this work lies in the 3D numerical modelling of the HVRM and the subsequent evaluation and analysis of its dynamic operation. Analytical and numerical 2D studies are less resource-intensive and time-consuming, and are more straightforward and rapid to analyse and interpret. However, they are constrained in their capacity to examine spatial, volumetric interactions and intricate dynamics such as flux studies where three 3D effects cannot be disregarded, winding end effects and the configuration and positioning of the interposed permanent magnet.展开更多
Marking 50 years of diplomatic ties,the EU-China relationship navigates complex dynamics as the EU balances partnership and competition,amidst shifting transatlantic landscapes.
1 Summary Mathematical modeling has become a cornerstone in understanding the complex dynamics of infectious diseases and chronic health conditions.With the advent of more refined computational techniques,researchers ...1 Summary Mathematical modeling has become a cornerstone in understanding the complex dynamics of infectious diseases and chronic health conditions.With the advent of more refined computational techniques,researchers are now able to incorporate intricate features such as delays,stochastic effects,fractional dynamics,variable-order systems,and uncertainty into epidemic models.These advancements not only improve predictive accuracy but also enable deeper insights into disease transmission,control,and policy-making.Tashfeen et al.展开更多
The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensiona...The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.展开更多
A problem of topology identification for complex dynamical networks is investigated in this paper. An adaptive observer is proposed to identify the topology of a complex dynamical networks based on the Lyapunov stabil...A problem of topology identification for complex dynamical networks is investigated in this paper. An adaptive observer is proposed to identify the topology of a complex dynamical networks based on the Lyapunov stability theory. Here the output of the network and the states of the observer are used to construct the updating law of the topology such that the communication resources from the network to its observer are saved. Some convergent criteria of the adaptive observer are derived in the form of linear inequality matrices. Several numerical examples are shown to demonstrate the effectiveness of the proposed observer.展开更多
In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the a...In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.展开更多
This paper presents a new robust adaptive synchronization method for a class of uncertain dynamical complex networks with network failures and coupling time-varying delays. Adaptive schemes are proposed to adjust cont...This paper presents a new robust adaptive synchronization method for a class of uncertain dynamical complex networks with network failures and coupling time-varying delays. Adaptive schemes are proposed to adjust controller parameters for the faulty network compensations, as well as to estimate the upper and lower bounds of delayed state errors and perturbations to compensate the effects of delay and perturbation on-line without assuming symmetry or irreducibility of networks. It is shown that, through Lyapunov stability theory, distributed adaptive controllers con- structed by the adaptive schemes are successful in ensuring the achievement of asymptotic synchronization of networks in the present of faulty and delayed networks, and perturbation inputs. A Chua＇s circuit network example is finally given to show the effectiveness of the proposed synchronization criteria.展开更多
This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is trans...This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.展开更多
This paper investigates the secure synchronization control problem for a class of cyber-physical systems(CPSs)with unknown system matrices and intermittent denial-of-service(DoS)attacks.For the attack free case,an opt...This paper investigates the secure synchronization control problem for a class of cyber-physical systems(CPSs)with unknown system matrices and intermittent denial-of-service(DoS)attacks.For the attack free case,an optimal control law consisting of a feedback control and a compensated feedforward control is proposed to achieve the synchronization,and the feedback control gain matrix is learned by iteratively solving an algebraic Riccati equation(ARE).For considering the attack cases,it is difficult to perform the stability analysis of the synchronization errors by using the existing Lyapunov function method due to the presence of unknown system matrices.In order to overcome this difficulty,a matrix polynomial replacement method is given and it is shown that,the proposed optimal control law can still guarantee the asymptotical convergence of synchronization errors if two inequality conditions related with the DoS attacks hold.Finally,two examples are given to illustrate the effectiveness of the proposed approaches.展开更多
This paper proposes a novel approach for fault diagnosis of a time-delay complex dynamical network. Unlike the other methods, assuming that the dynamics of the network can be described by a linear stochastic model, or...This paper proposes a novel approach for fault diagnosis of a time-delay complex dynamical network. Unlike the other methods, assuming that the dynamics of the network can be described by a linear stochastic model, or using the state variables of nodes in the network to design an adaptive observer, it only uses the output variable of the nodes to design an observer and an adaptive law of topology matrix in the observer of a complex network, leading to simple design of the observer and easy realisation of topology monitoring for the complex networks in real engineering. The proposed scheme can monitor any changes of the topology structure of a time-delay complex network. The effectiveness of this method is successfully demonstrated by virtue of a complex networks with Lorenz model.展开更多
This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer fu...This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.展开更多
This study establishes a low-carbon supply chain game model under the centralized decision situation and the decentralized decision situation considering the manufacturer risk-aversion behavior, and discusses the infl...This study establishes a low-carbon supply chain game model under the centralized decision situation and the decentralized decision situation considering the manufacturer risk-aversion behavior, and discusses the influence of the manufacturer risk-aversion behavior on the optimal decision, profit, coordination, and complex dynamics of the supply chain. We find that comparing with the risk-neutral decentralized decision, the increase of manufacturer's risk tolerance attitude can narrow the gap between the supply chain profit and the centralized decision, but it will further reduce the carbon emission reduction level. The increase of risk tolerance of the manufacturer and carbon tax will narrow the stable region of the system. Under this situation, the manufacturer should carefully adjust parameters to prevent the system from losing stability,especially the adjustment parameters for carbon emission reduction level. When the system is in a chaotic state, the increase of carbon tax rate makes the system show more complex dynamic characteristics. Under the chaotic state, it is difficult for the manufacturer to make correct price decision and carbon emission reduction strategy for the next period, which damages its profit, but increases the profit of the retailer and the supply chain. Finally, the carbon emission reduction cost-sharing contract is proposed to improve the carbon emission reduction level and the supply chain efficiency, achieving Pareto improvement. The stability region of the system is larger than that in the centralized decision situation, but the increase of the cost sharing coefficient will reduce the stability of the system in the decentralized decision-making situation.展开更多
This paper studies synchronization of all nodes in a fractional-order complex dynamic network. An adaptive control strategy for synchronizing a dynamic network is proposed. Based on the Lyapunov stability theory, this...This paper studies synchronization of all nodes in a fractional-order complex dynamic network. An adaptive control strategy for synchronizing a dynamic network is proposed. Based on the Lyapunov stability theory, this paper shows that tracking errors of all nodes in a fractional-order complex network converge to zero. This simple yet prac- tical scheme can be used in many networks such as small-world networks and scale-free networks. Unlike the existing methods which assume the coupling configuration among the nodes of the network with diffusivity, symmetry, balance, or irreducibility, in this case, these assumptions are unnecessary, and the proposed adaptive strategy is more feasible. Two examples are presented to illustrate effectiveness of the proposed method.展开更多
Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predomin...Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.展开更多
A new approach of adaptive distributed control is proposed for a class of networks with unknown time-varying coupling weights. The proposed approach ensures that the complex dynamical networks achieve asymptotical syn...A new approach of adaptive distributed control is proposed for a class of networks with unknown time-varying coupling weights. The proposed approach ensures that the complex dynamical networks achieve asymptotical synchronization and all the closed-loop signals are bounded. Furthermore, the coupling matrix is not assumed to be symmetric or irreducible and asymptotical synchronization can be achieved even when the graph of network is not connected. Finally, a simulation example shows the feasibility and effectiveness of the approach.展开更多
This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asy...This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities （LMIs）. The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.展开更多
基金Project supported by the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(Grant No.GZC20231050)the National Natural Science Foundation of China(Grant Nos.12175193 and 11905183)the 13th Five-year plan for Education Science Funding of Guangdong Province(Grant No.2021GXJK349)。
文摘For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.
文摘Timely detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meanings. We introduce a complexity measure for time series： the base-scale entropy. The definition directly applies to arbitrary real-word data. We illustrate our method on a practical speech signal and in a theoretical chaotic system. The results show that the simple and easily calculated measure of base-scale entropy can be effectively used to detect qualitative and quantitative dynamical changes.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62373197 and 61873326)。
文摘In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.
文摘This paper presents the work carried out to evaluate the dynamic performance of the Hybrid Variable Reluctance Motor (HVRM). The fourth-order Runge-Kutta integration algorithm was employed to solve the equations of the dynamic model, in conjunction with the three-dimensional finite element method. The 3D numerical data was calculated using Comsol Multiphysics, which accounts for the nonlinearity of the ferromagnetic material and the 3D nature of the HVRM. The outcomes of this study are precise and accurately predict the dynamic behaviour of the HVRM in terms of rotor position response, rotational speed and torque. The distinctive contribution of this work lies in the 3D numerical modelling of the HVRM and the subsequent evaluation and analysis of its dynamic operation. Analytical and numerical 2D studies are less resource-intensive and time-consuming, and are more straightforward and rapid to analyse and interpret. However, they are constrained in their capacity to examine spatial, volumetric interactions and intricate dynamics such as flux studies where three 3D effects cannot be disregarded, winding end effects and the configuration and positioning of the interposed permanent magnet.
文摘Marking 50 years of diplomatic ties,the EU-China relationship navigates complex dynamics as the EU balances partnership and competition,amidst shifting transatlantic landscapes.
文摘1 Summary Mathematical modeling has become a cornerstone in understanding the complex dynamics of infectious diseases and chronic health conditions.With the advent of more refined computational techniques,researchers are now able to incorporate intricate features such as delays,stochastic effects,fractional dynamics,variable-order systems,and uncertainty into epidemic models.These advancements not only improve predictive accuracy but also enable deeper insights into disease transmission,control,and policy-making.Tashfeen et al.
基金supported by the National Natural Science Foundation of China(Grant No.62303289)Tianyuan Fund for Mathematics of the National Natural Science Foundation of China(Grant No.12426105)+3 种基金the Scientific and Technological Innovation Programs(STIP)of Higher Education Institutions in Shanxi(Grant No.2024L022)Fundamental Research Program of Shanxi Province(Grant Nos.202403021222001 and 202203021222003)the“Wen Ying Young Scholars”Talent Project of Shanxi University(Grant Nos.138541088,138541090,and 138541127)Funded by Open Foundation of Hubei Key Laboratory of Applied Mathematics(Hubei University)(Grant No.HBAM202401).
文摘The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.
基金supported in part by the National Natural Science Foundation of China (Grant Nos.60874091 and 61104103)the Natural Science Fund for Colleges and Universities in Jiangsu Province,China (Grant No.10KJB120001)the Climbing Program of Nanjing University of Posts & Telecommunications,China (Grant Nos.NY210013 and NY210014)
文摘A problem of topology identification for complex dynamical networks is investigated in this paper. An adaptive observer is proposed to identify the topology of a complex dynamical networks based on the Lyapunov stability theory. Here the output of the network and the states of the observer are used to construct the updating law of the topology such that the communication resources from the network to its observer are saved. Some convergent criteria of the adaptive observer are derived in the form of linear inequality matrices. Several numerical examples are shown to demonstrate the effectiveness of the proposed observer.
文摘In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.
基金Project supported by the Funds for Creative Research Groups of China(Grant No.60821063)the National Basic Research Program of China(Grant No.2009CB320604)+2 种基金the National Natural Science Foundation of China(Grant No.60974043)the 111 Project(Grant No.B08015)the Science and Technology Research Project of the Educational Department of Liaoning Province of China(Grant No.2008S156)
文摘This paper presents a new robust adaptive synchronization method for a class of uncertain dynamical complex networks with network failures and coupling time-varying delays. Adaptive schemes are proposed to adjust controller parameters for the faulty network compensations, as well as to estimate the upper and lower bounds of delayed state errors and perturbations to compensate the effects of delay and perturbation on-line without assuming symmetry or irreducibility of networks. It is shown that, through Lyapunov stability theory, distributed adaptive controllers con- structed by the adaptive schemes are successful in ensuring the achievement of asymptotic synchronization of networks in the present of faulty and delayed networks, and perturbation inputs. A Chua＇s circuit network example is finally given to show the effectiveness of the proposed synchronization criteria.
基金the National Natural Science Foundation of China (No.60874024, 60574013).
文摘This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.
基金supported in part by the National Natural Science Foundation of China(61873050)the Fundamental Research Funds for the Central Universities(N180405022,N2004010)+1 种基金the Research Fund of State Key Laboratory of Synthetical Automation for Process Industries(2018ZCX14)Liaoning Revitalization Talents Program(XLYC1907088)。
文摘This paper investigates the secure synchronization control problem for a class of cyber-physical systems(CPSs)with unknown system matrices and intermittent denial-of-service(DoS)attacks.For the attack free case,an optimal control law consisting of a feedback control and a compensated feedforward control is proposed to achieve the synchronization,and the feedback control gain matrix is learned by iteratively solving an algebraic Riccati equation(ARE).For considering the attack cases,it is difficult to perform the stability analysis of the synchronization errors by using the existing Lyapunov function method due to the presence of unknown system matrices.In order to overcome this difficulty,a matrix polynomial replacement method is given and it is shown that,the proposed optimal control law can still guarantee the asymptotical convergence of synchronization errors if two inequality conditions related with the DoS attacks hold.Finally,two examples are given to illustrate the effectiveness of the proposed approaches.
基金supported in part by the Program for New Century Excellent Talents in University of China (Grant No. NCET-06-0510)the National Natural Science Foundation of China (Grant No. 60874091)
文摘This paper proposes a novel approach for fault diagnosis of a time-delay complex dynamical network. Unlike the other methods, assuming that the dynamics of the network can be described by a linear stochastic model, or using the state variables of nodes in the network to design an adaptive observer, it only uses the output variable of the nodes to design an observer and an adaptive law of topology matrix in the observer of a complex network, leading to simple design of the observer and easy realisation of topology monitoring for the complex networks in real engineering. The proposed scheme can monitor any changes of the topology structure of a time-delay complex network. The effectiveness of this method is successfully demonstrated by virtue of a complex networks with Lorenz model.
基金Project supported by the National Natural Science Foundation of China (Grant No 10832006)the Key Projects of Educational Ministry of China (Grant No 107110)
文摘This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.
基金Project supported by the Social Science Planning Project of Chongqing, China (Grant No. 2022BS069)the Science and Technology Research Project of Chongqing Education Committee, China (Grant No. KJQN202201140)+1 种基金the National Social Science Foundation of China (Grant No. 20&ZD155)the National Natural Science Foundation of China (Grant No. 72061003)。
文摘This study establishes a low-carbon supply chain game model under the centralized decision situation and the decentralized decision situation considering the manufacturer risk-aversion behavior, and discusses the influence of the manufacturer risk-aversion behavior on the optimal decision, profit, coordination, and complex dynamics of the supply chain. We find that comparing with the risk-neutral decentralized decision, the increase of manufacturer's risk tolerance attitude can narrow the gap between the supply chain profit and the centralized decision, but it will further reduce the carbon emission reduction level. The increase of risk tolerance of the manufacturer and carbon tax will narrow the stable region of the system. Under this situation, the manufacturer should carefully adjust parameters to prevent the system from losing stability,especially the adjustment parameters for carbon emission reduction level. When the system is in a chaotic state, the increase of carbon tax rate makes the system show more complex dynamic characteristics. Under the chaotic state, it is difficult for the manufacturer to make correct price decision and carbon emission reduction strategy for the next period, which damages its profit, but increases the profit of the retailer and the supply chain. Finally, the carbon emission reduction cost-sharing contract is proposed to improve the carbon emission reduction level and the supply chain efficiency, achieving Pareto improvement. The stability region of the system is larger than that in the centralized decision situation, but the increase of the cost sharing coefficient will reduce the stability of the system in the decentralized decision-making situation.
基金Project supported by the National Natural Science Foundation of China(Nos.11672231 and11672233)the Natural Science Foundation of Shaanxi Province(No.2016JM1010)+1 种基金the Fundamental Research Funds for the Central Universities(No.3102017AX008)the Seed Foundation of Innovation and Creation for Graduate Students at the Northwestern Polytechnical University of China(No.Z2017187)
文摘This paper studies synchronization of all nodes in a fractional-order complex dynamic network. An adaptive control strategy for synchronizing a dynamic network is proposed. Based on the Lyapunov stability theory, this paper shows that tracking errors of all nodes in a fractional-order complex network converge to zero. This simple yet prac- tical scheme can be used in many networks such as small-world networks and scale-free networks. Unlike the existing methods which assume the coupling configuration among the nodes of the network with diffusivity, symmetry, balance, or irreducibility, in this case, these assumptions are unnecessary, and the proposed adaptive strategy is more feasible. Two examples are presented to illustrate effectiveness of the proposed method.
文摘Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.
基金supported by Ph.D.Programs Foundation of Ministry of Education of China(Nos.JY0300137002 and20130203110021)Research Funds for the Central Universities(No.JB142001-6)
文摘A new approach of adaptive distributed control is proposed for a class of networks with unknown time-varying coupling weights. The proposed approach ensures that the complex dynamical networks achieve asymptotical synchronization and all the closed-loop signals are bounded. Furthermore, the coupling matrix is not assumed to be symmetric or irreducible and asymptotical synchronization can be achieved even when the graph of network is not connected. Finally, a simulation example shows the feasibility and effectiveness of the approach.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60274099)the National High Technology Research and Development Program of China (Grant No. 2004AA412030)
文摘This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities （LMIs）. The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.
