A dual-harmonic acceleration system is utilized to mitigate the space-charge effect in the rapid-cycling synchrotron of the China Spallation Neutron Source upgrade project(CSNS-II).A magnetic alloy(MA)-loaded cavity w...A dual-harmonic acceleration system is utilized to mitigate the space-charge effect in the rapid-cycling synchrotron of the China Spallation Neutron Source upgrade project(CSNS-II).A magnetic alloy(MA)-loaded cavity with a high accelerating gradient is developed to satisfy the requirements of dual-harmonic acceleration and provide the necessary second-harmonic cavity voltage.However,the MA-loaded cavity exhibits a wideband frequency response,resulting in numerous higher harmonics in the radio-frequency(RF)voltage.These higher harmonics are caused by both the beam-loading effect and distorted amplifier current,which distort the RF bucket,increase the power dissipation in the cavity,and lower the gradient.To address these issues,a multiharmonic independent feedback-control approach is implemented to compensate for higher harmonics.The effectiveness of this control strategy is validated experimentally.This study provides details regarding the feedback-control design and presents the commissioning results.展开更多
Controlling feedback control systems in continuous action spaces has always been a challenging problem.Nevertheless,reinforcement learning is mainly an area of artificial intelligence(AI)because it has been used in pr...Controlling feedback control systems in continuous action spaces has always been a challenging problem.Nevertheless,reinforcement learning is mainly an area of artificial intelligence(AI)because it has been used in process control for more than a decade.However,the existing algorithms are unable to provide satisfactory results.Therefore,this research uses a reinforcement learning(RL)algorithm to manage the control system.We propose an adaptive speed control of the motor system based on depth deterministic strategy gradient(DDPG).The actor-critic scenario using DDPG is implemented to build the RL agent.In addition,a framework has been created for traditional feedback control systems to make RL implementation easier for control systems.The RL algorithms are robust and proficient in using trial and error to search for the best strategy.Our proposed algorithm is a deep deterministic policy gradient,in which a large amount of training data trains the agent.Once the system is trained,the agent can automatically adjust the control parameters.The algorithm has been developed using Python 3.6 and the simulation results are evaluated in the MATLAB/Simulink environment.The performance of the proposed RL algorithm is compared with a proportional integral derivative(PID)controller and a linear quadratic regulator(LQR)controller.The simulation results of the proposed scheme are promising for the feedback control problems.展开更多
It is well accepted that lower hybrid current drive （LHCD） is the most efficient method for non-inductive current drive in fusion devices and the effect of the current drive is dependent on not only microwave power ...It is well accepted that lower hybrid current drive （LHCD） is the most efficient method for non-inductive current drive in fusion devices and the effect of the current drive is dependent on not only microwave power but also its grill phase shift. This paper presents a new kind of feedback control system for antenna phase difference in LHCD experiments. In this highspeed control system, a lot of new technologies and methods are incorporated. The results of the experiments show a very good agreement with the system design.展开更多
Through a detailed analysis of the construction of HT-7, a decoupling model for heating field and vertical field is given. This paper presents a simple introduction of its basic structure. And with a practical design,...Through a detailed analysis of the construction of HT-7, a decoupling model for heating field and vertical field is given. This paper presents a simple introduction of its basic structure. And with a practical design, this model has been successfully applied to the device, procuring a very good controlling of the plasma parameters of HT-7. The performance of individual feedback systems is also analyzed in detail.展开更多
Ion cyclotron wave resonance heating(ICRH) is one of the most important auxiliary methods to heat plasma in the Experimental Advanced Superconducting Tokamak(EAST). Several megawatts of power is transmitted through se...Ion cyclotron wave resonance heating(ICRH) is one of the most important auxiliary methods to heat plasma in the Experimental Advanced Superconducting Tokamak(EAST). Several megawatts of power is transmitted through separate coaxial lines and coupled with the plasma through arrays of loop antennas. The parameters of the ICRH system, including the injected power and phasing between antenna straps, are critical to the coupling efficiency of the power as well as the resulting impact on the heating efficiency. In this paper, we present a system for feedback control of the phase between the current straps and the ICRH power on EAST. The feedback control system was tested using both a matched dummy load and a plasma load, and it successfully maintained stable operation in the 2016 EAST campaign. Good control of the injected power and wave phases was achieved during edgelocalized mode operation.展开更多
The HT-7 is a superconducting tokamak in China used to make researches on the controlled nuclear fusion as a national project for the fusion research. The plasma density feedback control subsystem is the one of the su...The HT-7 is a superconducting tokamak in China used to make researches on the controlled nuclear fusion as a national project for the fusion research. The plasma density feedback control subsystem is the one of the subsystems of the distributed control system in HT-7 tokamak (HT7DCS). The main function of the subsystem is to control the plasma density on real-time. For this reason, the real-time capability and good stability are the most significant factors, which will influence the control results. Since the former plasma density feedback control system (FPDFCS) based on Windows operation system could not fulfill such requirements well, a new subsystem has to be developed. The paper describes the upgrade of the plasma density feedback control system (UPDFCS), based on the dual operation system (Windows and Linux), in detail.展开更多
In this paper,a recurrent neural network(RNN)is used to estimate uncertainties and implement feedback control for nonlinear dynamic systems.The neural network approximates the uncertainties related to unmodeled dynami...In this paper,a recurrent neural network(RNN)is used to estimate uncertainties and implement feedback control for nonlinear dynamic systems.The neural network approximates the uncertainties related to unmodeled dynamics,parametric variations,and external disturbances.The RNN has a single hidden layer and uses the tracking error and the output as feedback to estimate the disturbance.The RNN weights are online adapted,and the adaptation laws are developed from the stability analysis of the controlled system with the RNN estimation.The used activation function,at the hidden layer,has an expression that simplifies the adaptation laws from the stability analysis.It is found that the adaptive RNN enhances the tracking performance of the feedback controller at the transient and steady state responses.The proposed RNN based feedback control is applied to a DC–DC converter for current regulation.Simulation and experimental results are provided to show its effectiveness.Compared to the feedforward neural network and the conventional feedback control,the RNN based feedback control provides good tracking performance.展开更多
In order to study the dynamic characteristics of the single-frequency signal through the nonlinear control system,the system control mode,the outer excitation patterns of the model and the amplitude are investigated b...In order to study the dynamic characteristics of the single-frequency signal through the nonlinear control system,the system control mode,the outer excitation patterns of the model and the amplitude are investigated by using the methods of the nonlinear dynamical analysis. The time-domain diagram,power spectrum,phase diagram and the largest Lyapunov exponent obtained from the process of the signal propagate through different control module are given. The researches on different control systems demonstrate that: after single-frequency signal goes through the nonlinear controller,it is still non-chaotic although the output contains more frequency components; but with the feedback and the external perturbation,the output is a continuous broadband spectrum and the result shows that there is chaos. The energy of the input signal reduces with some appropriate parameters. Therefore,the control system of the nonlinear feedback is a good way to broaden the spectrum of output with inputting a single-frequency signal.展开更多
Based on the suitably defined multivariable version of Kranc operators and the extended input and output vectors, the multirate sampling plant is transformed to a equivalent time invariant single rate one, then the t...Based on the suitably defined multivariable version of Kranc operators and the extended input and output vectors, the multirate sampling plant is transformed to a equivalent time invariant single rate one, then the transfer function model of the multivariable multirate sampling plant is obtained. By combining this plant model with the time invariant description of the multirate controller in terms of extended vectors, the closed loop transfer function model of the multirate feedback control system can be determinated. This transfer function model has a very simple structure, and can be used as a basis for the analysis and synthesis of the multirate sampling feedback control systems in the frequency domain.展开更多
The plasma density feedback control system（PDFCS） has been established on the Joint Texas Experimental Tokamak（J-TEXT） for meeting the need for an accurate plasma density in physical experiments.It consists of a d...The plasma density feedback control system（PDFCS） has been established on the Joint Texas Experimental Tokamak（J-TEXT） for meeting the need for an accurate plasma density in physical experiments.It consists of a density measurement subsystem,a feedback control subsystem and a gas puffing subsystem.According to the characteristic of the gas puffing system,a voltage amplitude control mode has been applied in the feedback control strategy,which is accomplished by the proportion,integral and differential（PID） controller.In this system,the quantity calibration of gas injection,adjusted responding to the change of the density signal,has been carried out.Some experimental results are shown and discussed.展开更多
As the limit of time and budget etc, the control system of HL-2A just could be operated in programmed discharge when HL-2A was checked and accepted in 2002. Recent years, many subsystem of HL-2A have been improved in ...As the limit of time and budget etc, the control system of HL-2A just could be operated in programmed discharge when HL-2A was checked and accepted in 2002. Recent years, many subsystem of HL-2A have been improved in functions and performances. And the demand for experiment of HL-2A is becoming more and more higher in plasma discharge parameters. So it＇s necessary to develop a plasma feedback control system （ FBCS ） which has enough functions and good stability and reliability to satisfy the demand of experiment on HL-2A.展开更多
The paper presents an adaptive controller formulated for a class of nonaffine discrete-time systems with non-strict forms and unknown dynamics.The controller operates based solely on the measured output,thus obviating...The paper presents an adaptive controller formulated for a class of nonaffine discrete-time systems with non-strict forms and unknown dynamics.The controller operates based solely on the measured output,thus obviating the need for knowledge of the physical order of the controlled plant.Utilizing an ideal solution and equivalent dynamics,the approach integrates an adaptive network with feedback and robust controllers to establish a closed-loop system.A learning law is derived under practical conditions of the designed parameters,ensuring effective closed-loop performance based on pure-output feedback.The controller’s effectiveness is validated through both numerical and experimental systems,with results meeting the conditions specified in the main theorem.Comparative analysis highlights the controller’s highly satisfactory performance and its advantages.This research offers a promising approach to adaptive control for discrete-time systems with non-strict dynamics,providing practical solutions for systems with unknown dynamics and indeterminate system order.展开更多
The problem of time delay speed feedback in the control loop is considered here.Its effects on the linear stability and dynamic behavior of the maglev system are investigated.It is found that a Hopf bifurcation can ta...The problem of time delay speed feedback in the control loop is considered here.Its effects on the linear stability and dynamic behavior of the maglev system are investigated.It is found that a Hopf bifurcation can take place when the time delay exceeds certain values.The stability condition of the maglev system with the time delay is acquired.The direction and stability of the Hopf bifurcation are determined by constructing a center manifold and by applying the normal form method.Finally,numerical simulations are performed to verify the analytical result.展开更多
The linear systems affected by additive external sinusoidal disturbances is studied. The problem is to damp this forced oscillation in an optimal fashion. The main result of this paper is a new design approach is prop...The linear systems affected by additive external sinusoidal disturbances is studied. The problem is to damp this forced oscillation in an optimal fashion. The main result of this paper is a new design approach is proposed of realizable feedforward and feedback optimal control law for a linear time invariant system with sinusoidal disturbances. The algorithm of solving the optimal control law is given. It is shown that the control law is easily realized and is robust with respect to errors produced by the external sinusoidal disturbances through simulation results.展开更多
This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to ac...This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.展开更多
This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapun...This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov expo- nents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench （EWB）. Numerical simulations are presented to show these results.展开更多
The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are de...The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.展开更多
The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are...The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality （LMI）. A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.展开更多
This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition ...This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11875270 and 12205317)the Youth Innovation Promotion Association,Chinese Academy of Sciences(No.2018015)。
文摘A dual-harmonic acceleration system is utilized to mitigate the space-charge effect in the rapid-cycling synchrotron of the China Spallation Neutron Source upgrade project(CSNS-II).A magnetic alloy(MA)-loaded cavity with a high accelerating gradient is developed to satisfy the requirements of dual-harmonic acceleration and provide the necessary second-harmonic cavity voltage.However,the MA-loaded cavity exhibits a wideband frequency response,resulting in numerous higher harmonics in the radio-frequency(RF)voltage.These higher harmonics are caused by both the beam-loading effect and distorted amplifier current,which distort the RF bucket,increase the power dissipation in the cavity,and lower the gradient.To address these issues,a multiharmonic independent feedback-control approach is implemented to compensate for higher harmonics.The effectiveness of this control strategy is validated experimentally.This study provides details regarding the feedback-control design and presents the commissioning results.
基金This work was supported by the King Saud University in Riyadh,Saudi Arabia,through the Researchers Supporting Project Number(RSP-2021/387).
文摘Controlling feedback control systems in continuous action spaces has always been a challenging problem.Nevertheless,reinforcement learning is mainly an area of artificial intelligence(AI)because it has been used in process control for more than a decade.However,the existing algorithms are unable to provide satisfactory results.Therefore,this research uses a reinforcement learning(RL)algorithm to manage the control system.We propose an adaptive speed control of the motor system based on depth deterministic strategy gradient(DDPG).The actor-critic scenario using DDPG is implemented to build the RL agent.In addition,a framework has been created for traditional feedback control systems to make RL implementation easier for control systems.The RL algorithms are robust and proficient in using trial and error to search for the best strategy.Our proposed algorithm is a deep deterministic policy gradient,in which a large amount of training data trains the agent.Once the system is trained,the agent can automatically adjust the control parameters.The algorithm has been developed using Python 3.6 and the simulation results are evaluated in the MATLAB/Simulink environment.The performance of the proposed RL algorithm is compared with a proportional integral derivative(PID)controller and a linear quadratic regulator(LQR)controller.The simulation results of the proposed scheme are promising for the feedback control problems.
基金Meg-science Engineering Project of the Chinese Academy of Sciences
文摘It is well accepted that lower hybrid current drive （LHCD） is the most efficient method for non-inductive current drive in fusion devices and the effect of the current drive is dependent on not only microwave power but also its grill phase shift. This paper presents a new kind of feedback control system for antenna phase difference in LHCD experiments. In this highspeed control system, a lot of new technologies and methods are incorporated. The results of the experiments show a very good agreement with the system design.
文摘Through a detailed analysis of the construction of HT-7, a decoupling model for heating field and vertical field is given. This paper presents a simple introduction of its basic structure. And with a practical design, this model has been successfully applied to the device, procuring a very good controlling of the plasma parameters of HT-7. The performance of individual feedback systems is also analyzed in detail.
基金supported in part by the National Magnetic Confinement Fusion Science Program(No.2015GB101001)the National Natural Science Foundation of China(Nos.11375236 and11375235)
文摘Ion cyclotron wave resonance heating(ICRH) is one of the most important auxiliary methods to heat plasma in the Experimental Advanced Superconducting Tokamak(EAST). Several megawatts of power is transmitted through separate coaxial lines and coupled with the plasma through arrays of loop antennas. The parameters of the ICRH system, including the injected power and phasing between antenna straps, are critical to the coupling efficiency of the power as well as the resulting impact on the heating efficiency. In this paper, we present a system for feedback control of the phase between the current straps and the ICRH power on EAST. The feedback control system was tested using both a matched dummy load and a plasma load, and it successfully maintained stable operation in the 2016 EAST campaign. Good control of the injected power and wave phases was achieved during edgelocalized mode operation.
文摘The HT-7 is a superconducting tokamak in China used to make researches on the controlled nuclear fusion as a national project for the fusion research. The plasma density feedback control subsystem is the one of the subsystems of the distributed control system in HT-7 tokamak (HT7DCS). The main function of the subsystem is to control the plasma density on real-time. For this reason, the real-time capability and good stability are the most significant factors, which will influence the control results. Since the former plasma density feedback control system (FPDFCS) based on Windows operation system could not fulfill such requirements well, a new subsystem has to be developed. The paper describes the upgrade of the plasma density feedback control system (UPDFCS), based on the dual operation system (Windows and Linux), in detail.
基金supported in part by Khalifa University of Science and Technology (KUST),United Arab Emirates under Award CIRA-2020-013.
文摘In this paper,a recurrent neural network(RNN)is used to estimate uncertainties and implement feedback control for nonlinear dynamic systems.The neural network approximates the uncertainties related to unmodeled dynamics,parametric variations,and external disturbances.The RNN has a single hidden layer and uses the tracking error and the output as feedback to estimate the disturbance.The RNN weights are online adapted,and the adaptation laws are developed from the stability analysis of the controlled system with the RNN estimation.The used activation function,at the hidden layer,has an expression that simplifies the adaptation laws from the stability analysis.It is found that the adaptive RNN enhances the tracking performance of the feedback controller at the transient and steady state responses.The proposed RNN based feedback control is applied to a DC–DC converter for current regulation.Simulation and experimental results are provided to show its effectiveness.Compared to the feedforward neural network and the conventional feedback control,the RNN based feedback control provides good tracking performance.
基金Sponsored by Basic Research Development Program(Grant No.7131107)the National Natural Science Foundation of China(Grant No.51206101)
文摘In order to study the dynamic characteristics of the single-frequency signal through the nonlinear control system,the system control mode,the outer excitation patterns of the model and the amplitude are investigated by using the methods of the nonlinear dynamical analysis. The time-domain diagram,power spectrum,phase diagram and the largest Lyapunov exponent obtained from the process of the signal propagate through different control module are given. The researches on different control systems demonstrate that: after single-frequency signal goes through the nonlinear controller,it is still non-chaotic although the output contains more frequency components; but with the feedback and the external perturbation,the output is a continuous broadband spectrum and the result shows that there is chaos. The energy of the input signal reduces with some appropriate parameters. Therefore,the control system of the nonlinear feedback is a good way to broaden the spectrum of output with inputting a single-frequency signal.
文摘Based on the suitably defined multivariable version of Kranc operators and the extended input and output vectors, the multirate sampling plant is transformed to a equivalent time invariant single rate one, then the transfer function model of the multivariable multirate sampling plant is obtained. By combining this plant model with the time invariant description of the multirate controller in terms of extended vectors, the closed loop transfer function model of the multirate feedback control system can be determinated. This transfer function model has a very simple structure, and can be used as a basis for the analysis and synthesis of the multirate sampling feedback control systems in the frequency domain.
基金supported by the National Magnetic Confinement Fusion Science Program(Nos.2014GB103001 and 2013GB106001)National Natural Science Foundation of China(Nos.11305070 and 11105028)
文摘The plasma density feedback control system（PDFCS） has been established on the Joint Texas Experimental Tokamak（J-TEXT） for meeting the need for an accurate plasma density in physical experiments.It consists of a density measurement subsystem,a feedback control subsystem and a gas puffing subsystem.According to the characteristic of the gas puffing system,a voltage amplitude control mode has been applied in the feedback control strategy,which is accomplished by the proportion,integral and differential（PID） controller.In this system,the quantity calibration of gas injection,adjusted responding to the change of the density signal,has been carried out.Some experimental results are shown and discussed.
文摘As the limit of time and budget etc, the control system of HL-2A just could be operated in programmed discharge when HL-2A was checked and accepted in 2002. Recent years, many subsystem of HL-2A have been improved in functions and performances. And the demand for experiment of HL-2A is becoming more and more higher in plasma discharge parameters. So it＇s necessary to develop a plasma feedback control system （ FBCS ） which has enough functions and good stability and reliability to satisfy the demand of experiment on HL-2A.
文摘The paper presents an adaptive controller formulated for a class of nonaffine discrete-time systems with non-strict forms and unknown dynamics.The controller operates based solely on the measured output,thus obviating the need for knowledge of the physical order of the controlled plant.Utilizing an ideal solution and equivalent dynamics,the approach integrates an adaptive network with feedback and robust controllers to establish a closed-loop system.A learning law is derived under practical conditions of the designed parameters,ensuring effective closed-loop performance based on pure-output feedback.The controller’s effectiveness is validated through both numerical and experimental systems,with results meeting the conditions specified in the main theorem.Comparative analysis highlights the controller’s highly satisfactory performance and its advantages.This research offers a promising approach to adaptive control for discrete-time systems with non-strict dynamics,providing practical solutions for systems with unknown dynamics and indeterminate system order.
基金Supported by National Natural Science Foundation of China(604040037 and Fork Ying-Dong Education Foundation(94028)
文摘The problem of time delay speed feedback in the control loop is considered here.Its effects on the linear stability and dynamic behavior of the maglev system are investigated.It is found that a Hopf bifurcation can take place when the time delay exceeds certain values.The stability condition of the maglev system with the time delay is acquired.The direction and stability of the Hopf bifurcation are determined by constructing a center manifold and by applying the normal form method.Finally,numerical simulations are performed to verify the analytical result.
文摘The linear systems affected by additive external sinusoidal disturbances is studied. The problem is to damp this forced oscillation in an optimal fashion. The main result of this paper is a new design approach is proposed of realizable feedforward and feedback optimal control law for a linear time invariant system with sinusoidal disturbances. The algorithm of solving the optimal control law is given. It is shown that the control law is easily realized and is robust with respect to errors produced by the external sinusoidal disturbances through simulation results.
文摘This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.
基金Project supported by the National Natural Science Foundations of China (Grant Nos. 70571030 and 90610031)the Society Science Foundation from Ministry of Education of China (Grant No. 08JA790057)the Advanced Talents’ Foundation and Student’s Foundation of Jiangsu University (Grant Nos. 07JDG054 and 07A075)
文摘This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov expo- nents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench （EWB）. Numerical simulations are presented to show these results.
文摘The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.
基金supported by National Natural Science Foundation of China (No.60674092)
文摘The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality （LMI）. A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.
基金partially supported by National Natural Science Foundation of China(61290322,61273222,61322303,61473248,61403335)Hebei Province Applied Basis Research Project(15967629D)Top Talents Project of Hebei Province and Yanshan University Project(13LGA020)
基金supported by the National Natural Science Foundation of China (Grant No. 60702023)Natural Science Foundation of Zhejiang Province (Grant No. Y107440)
文摘This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.
