In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the le...In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.展开更多
Two second-order consensus algorithms with a time-vary reference state without relative velocity measurements are proposed in a directed topology. Necessary and sufficient conditions are presented to ensure second-ord...Two second-order consensus algorithms with a time-vary reference state without relative velocity measurements are proposed in a directed topology. Necessary and sufficient conditions are presented to ensure second-order consensus. It is shown that all the coupling strengths and the ei- genvalues of the Laplacian matrix play important roles in reaching consensus. Specially when all non- zero eigenvalues of the Laplacian matrix are real, consensus can be achieved if and only if the cou- pling strengths are positive and the directed topology has a spanning tree for the first algorithm, and for the second one, consensus can be achieved if and only if the coupling strengths are positive. Fi- nally, simulation examples are presented to verify the theoretical analysis.展开更多
Continuous control protocols are extensively utilized in traditional MASs,in which information needs to be transmitted among agents consecutively,therefore resulting in excessive consumption of limited resources.To de...Continuous control protocols are extensively utilized in traditional MASs,in which information needs to be transmitted among agents consecutively,therefore resulting in excessive consumption of limited resources.To decrease the control cost,based on ISC,several LFC problems are investigated for second-order MASs without and with time delay,respectively.Firstly,an intermittent sampled controller is designed,and a sufficient and necessary condition is derived,under which state errors between the leader and all the followers approach zero asymptotically.Considering that time delay is inevitable,a new protocol is proposed to deal with the time-delay situation.The error system’s stability is analyzed using the Schur stability theorem,and sufficient and necessary conditions for LFC are obtained,which are closely associated with the coupling gain,the system parameters,and the network structure.Furthermore,for the case where the current position and velocity information are not available,a distributed protocol is designed that depends only on the sampled position information.The sufficient and necessary conditions for LFC are also given.The results show that second-order MASs can achieve the LFC if and only if the system parameters satisfy the inequalities proposed in the paper.Finally,the correctness of the obtained results is verified by numerical simulations.展开更多
In this paper,we investigate the phenomena of electromagnetically induced transparency and the generation of second-order sideband in a Laguerre–Gaussian cavity optorotational system with a Kerr nonlinear medium.Usin...In this paper,we investigate the phenomena of electromagnetically induced transparency and the generation of second-order sideband in a Laguerre–Gaussian cavity optorotational system with a Kerr nonlinear medium.Using the perturbation method,we analyze the first-and second-order sideband generations in the output field from the system under the actions of a strong control field and a weak probe field.Numerical simulations show that the Kerr nonlinearity can lead to the occurrence of the asymmetric line shape in the transmission of the probe field.Comparing with traditional scheme for generating the second-order sideband,our spectral shape of the second-order sideband is amplified and becomes asymmetric,which has potential applications in precision measurement,high-sensitivity devices,and frequency conversion.展开更多
Reinforcement learning behavioral control(RLBC)is limited to an individual agent without any swarm mission,because it models the behavior priority learning as a Markov decision process.In this paper,a novel multi-agen...Reinforcement learning behavioral control(RLBC)is limited to an individual agent without any swarm mission,because it models the behavior priority learning as a Markov decision process.In this paper,a novel multi-agent reinforcement learning behavioral control(MARLBC)method is proposed to overcome such limitations by implementing joint learning.Specifically,a multi-agent reinforcement learning mission supervisor(MARLMS)is designed for a group of nonlinear second-order systems to assign the behavior priorities at the decision layer.Through modeling behavior priority switching as a cooperative Markov game,the MARLMS learns an optimal joint behavior priority to reduce dependence on human intelligence and high-performance computing hardware.At the control layer,a group of second-order reinforcement learning controllers are designed to learn the optimal control policies to track position and velocity signals simultaneously.In particular,input saturation constraints are strictly implemented via designing a group of adaptive compensators.Numerical simulation results show that the proposed MARLBC has a lower switching frequency and control cost than finite-time and fixed-time behavioral control and RLBC methods.展开更多
Polarization-dependent second harmonic generation is a widely utilized technique for characterizing symmetry.However,in collinear reflective geometry,the essential beam-splitting device significantly influences both t...Polarization-dependent second harmonic generation is a widely utilized technique for characterizing symmetry.However,in collinear reflective geometry,the essential beam-splitting device significantly influences both the polarization state of the fundamental and harmonic beams,thereby affecting the accuracy of the obtained second-order nonlinear susceptibility.Here,we propose a data correction method to solve this problem to obtain accurate secondorder nonlinear susceptibility.The feasibility and generality of the method are demonstrated through theoretical and experimental validation.展开更多
We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system.We show that in the presence of the Kerr effect,as the strength of the ...We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system.We show that in the presence of the Kerr effect,as the strength of the Kerr effect increases,the absorption curve exhibits an asymmetric-symmetric-asymmetric transition,and the zero absorption point shifts with the increase of the Kerr effect.Furthermore,by changing the strength of the Kerr effect,we can control the width of the transparent window,and the position of the zero-absorption point and meanwhile change the left and right width of the absorption peak.The asymmetry absorption curve can be employed to improve the quality factor of the cavity when the frequency detuning is tuned to be around the right peak.The simple dependence of the zeroabsorption point on the strength of Kerr effect suggests that the strength of Kerr effect can be measured by measuring the position of the zero-absorption point in a possible application.展开更多
To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregress...To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.展开更多
In the cascaded H-bridge inverter(CHBI)with supercapacitor and dc-dc stage,inherent second-order harmonic power flows through each submodule(SM),causing fluctuations in both the dc-link voltage and the dc-dc current.T...In the cascaded H-bridge inverter(CHBI)with supercapacitor and dc-dc stage,inherent second-order harmonic power flows through each submodule(SM),causing fluctuations in both the dc-link voltage and the dc-dc current.There exist limitations in handling these fluctuations at variable output frequencies when employing proportional-integral(PI)control to the dc-dc stage.This paper aims to coordinately control these second-order harmonic voltage and current fluctuations in the CHBI.The presented method configures a specific second-order harmonic voltage reference,equipped with a maximum voltage fluctuation constraint and a suitable phase,for the dc-dc stage.A PI-resonant controller is used to track the configured reference.This allows for regulating the second-order harmonic fluctuation in the average dc-link voltage among the SMs within a certain value.Importantly,the second-order harmonic fluctuation in the dc-dc current can also be reduced.Simulation and experimental results demonstrate the effectiveness of the presented method.展开更多
In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilize...In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.展开更多
The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigne...The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigned to particular phonon branches and the points in the Brillouin zone from which the scattering originates.There exists a doublet at 626/636cm -1 with energy difference about 10cm -1 in both n- and p-type 4H-SiC,which is similar to the doublet structure with the same energy difference founded in hexagonal GaN,ZnO, and AlN.The cutoff frequency at 1926cm -1 of the second-order Raman is not the overtone of the A 1(LO) peak of the n-type doping 4H-SiC,but that of the undoping one.The second-order Raman spectrum of 4H-SiC can hardly be affected by doping species or doping density.展开更多
In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operato...In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.展开更多
When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be op...When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.展开更多
In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that se...In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method.展开更多
This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different ...This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.展开更多
Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-...Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions respectively, consensus criterions in the form of linear matrix inequality （LMI） are obtained for the system with time-varying communication delays under static interconnection topology con- verging to the leader＇s states. Moreover, the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovskii functional. Numerical simulations present the correctness of the results.展开更多
Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop ...Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.展开更多
In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to for...In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles（UAVs） is given to demonstrate the feasibility of theoretical results.展开更多
The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,...The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.展开更多
基金supported by the National Natural Science Foundation of China(61203354)
文摘In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.
基金Supported by the National Natural Science Foundation of China(61074031)
文摘Two second-order consensus algorithms with a time-vary reference state without relative velocity measurements are proposed in a directed topology. Necessary and sufficient conditions are presented to ensure second-order consensus. It is shown that all the coupling strengths and the ei- genvalues of the Laplacian matrix play important roles in reaching consensus. Specially when all non- zero eigenvalues of the Laplacian matrix are real, consensus can be achieved if and only if the cou- pling strengths are positive and the directed topology has a spanning tree for the first algorithm, and for the second one, consensus can be achieved if and only if the coupling strengths are positive. Fi- nally, simulation examples are presented to verify the theoretical analysis.
基金supported by the National Natural Science Foundation of China under Grants 62476138 and 42375016.
文摘Continuous control protocols are extensively utilized in traditional MASs,in which information needs to be transmitted among agents consecutively,therefore resulting in excessive consumption of limited resources.To decrease the control cost,based on ISC,several LFC problems are investigated for second-order MASs without and with time delay,respectively.Firstly,an intermittent sampled controller is designed,and a sufficient and necessary condition is derived,under which state errors between the leader and all the followers approach zero asymptotically.Considering that time delay is inevitable,a new protocol is proposed to deal with the time-delay situation.The error system’s stability is analyzed using the Schur stability theorem,and sufficient and necessary conditions for LFC are obtained,which are closely associated with the coupling gain,the system parameters,and the network structure.Furthermore,for the case where the current position and velocity information are not available,a distributed protocol is designed that depends only on the sampled position information.The sufficient and necessary conditions for LFC are also given.The results show that second-order MASs can achieve the LFC if and only if the system parameters satisfy the inequalities proposed in the paper.Finally,the correctness of the obtained results is verified by numerical simulations.
基金supported by the National Natural Science Foundation of China(Grant Nos.12174344 and 12175199)Foundation of Department of Science and Technology of Zhejiang Province(Grant No.2022R52047)。
文摘In this paper,we investigate the phenomena of electromagnetically induced transparency and the generation of second-order sideband in a Laguerre–Gaussian cavity optorotational system with a Kerr nonlinear medium.Using the perturbation method,we analyze the first-and second-order sideband generations in the output field from the system under the actions of a strong control field and a weak probe field.Numerical simulations show that the Kerr nonlinearity can lead to the occurrence of the asymmetric line shape in the transmission of the probe field.Comparing with traditional scheme for generating the second-order sideband,our spectral shape of the second-order sideband is amplified and becomes asymmetric,which has potential applications in precision measurement,high-sensitivity devices,and frequency conversion.
基金Project supported by the National Natural Science Foundation of China(No.92367109)。
文摘Reinforcement learning behavioral control(RLBC)is limited to an individual agent without any swarm mission,because it models the behavior priority learning as a Markov decision process.In this paper,a novel multi-agent reinforcement learning behavioral control(MARLBC)method is proposed to overcome such limitations by implementing joint learning.Specifically,a multi-agent reinforcement learning mission supervisor(MARLMS)is designed for a group of nonlinear second-order systems to assign the behavior priorities at the decision layer.Through modeling behavior priority switching as a cooperative Markov game,the MARLMS learns an optimal joint behavior priority to reduce dependence on human intelligence and high-performance computing hardware.At the control layer,a group of second-order reinforcement learning controllers are designed to learn the optimal control policies to track position and velocity signals simultaneously.In particular,input saturation constraints are strictly implemented via designing a group of adaptive compensators.Numerical simulation results show that the proposed MARLBC has a lower switching frequency and control cost than finite-time and fixed-time behavioral control and RLBC methods.
基金This work was supported by the National Natural Science Foundation of China(No.U2230203)the Fundamental Research Funds for the Central Universities.
文摘Polarization-dependent second harmonic generation is a widely utilized technique for characterizing symmetry.However,in collinear reflective geometry,the essential beam-splitting device significantly influences both the polarization state of the fundamental and harmonic beams,thereby affecting the accuracy of the obtained second-order nonlinear susceptibility.Here,we propose a data correction method to solve this problem to obtain accurate secondorder nonlinear susceptibility.The feasibility and generality of the method are demonstrated through theoretical and experimental validation.
基金Supported by the Key Scientific Research Plan of Colleges and Universities in Henan Province(23B140006)the National Natural Science Foundation of China(11965017)。
文摘We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system.We show that in the presence of the Kerr effect,as the strength of the Kerr effect increases,the absorption curve exhibits an asymmetric-symmetric-asymmetric transition,and the zero absorption point shifts with the increase of the Kerr effect.Furthermore,by changing the strength of the Kerr effect,we can control the width of the transparent window,and the position of the zero-absorption point and meanwhile change the left and right width of the absorption peak.The asymmetry absorption curve can be employed to improve the quality factor of the cavity when the frequency detuning is tuned to be around the right peak.The simple dependence of the zeroabsorption point on the strength of Kerr effect suggests that the strength of Kerr effect can be measured by measuring the position of the zero-absorption point in a possible application.
基金The National Key Research and Development Program of China under contract No.2023YFC3107701the National Natural Science Foundation of China under contract No.42375143.
文摘To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.
基金supported by the National Key Research and Development Program of China under Grant 2023YFB2407400。
文摘In the cascaded H-bridge inverter(CHBI)with supercapacitor and dc-dc stage,inherent second-order harmonic power flows through each submodule(SM),causing fluctuations in both the dc-link voltage and the dc-dc current.There exist limitations in handling these fluctuations at variable output frequencies when employing proportional-integral(PI)control to the dc-dc stage.This paper aims to coordinately control these second-order harmonic voltage and current fluctuations in the CHBI.The presented method configures a specific second-order harmonic voltage reference,equipped with a maximum voltage fluctuation constraint and a suitable phase,for the dc-dc stage.A PI-resonant controller is used to track the configured reference.This allows for regulating the second-order harmonic fluctuation in the average dc-link voltage among the SMs within a certain value.Importantly,the second-order harmonic fluctuation in the dc-dc current can also be reduced.Simulation and experimental results demonstrate the effectiveness of the presented method.
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
基金supported by National Natural Science Foundation of China (No.60504007)the PhD Programs Foundation of Ministry of Educationof China (No.20070286040)the Scientific Research Foundation of Graduate School of Southeast University
文摘In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.
文摘The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigned to particular phonon branches and the points in the Brillouin zone from which the scattering originates.There exists a doublet at 626/636cm -1 with energy difference about 10cm -1 in both n- and p-type 4H-SiC,which is similar to the doublet structure with the same energy difference founded in hexagonal GaN,ZnO, and AlN.The cutoff frequency at 1926cm -1 of the second-order Raman is not the overtone of the A 1(LO) peak of the n-type doping 4H-SiC,but that of the undoping one.The second-order Raman spectrum of 4H-SiC can hardly be affected by doping species or doping density.
文摘In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.
基金Special Item of National Major Scientific Apparatus Development(No.2013YQ140431)
文摘When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.
基金The National Natural Science Foundation of China(No.61231002,61273266,61375028)the Ph.D.Programs Foundation of Ministry of Education of China(No.20110092130004)
文摘In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70571059)
文摘This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.
基金supported by the Fundamental Research Funds for the Central Universities(JUSRP11020)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20090093120006)
文摘Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions respectively, consensus criterions in the form of linear matrix inequality （LMI） are obtained for the system with time-varying communication delays under static interconnection topology con- verging to the leader＇s states. Moreover, the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovskii functional. Numerical simulations present the correctness of the results.
文摘Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.
基金co-supported by the National Natural Science Foundation of China (Nos. 61333011, 91216304 and 61121003)
文摘In this paper, formation tracking control problems for second-order multi-agent systems（MASs） with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neighboring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, conditions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles（UAVs） is given to demonstrate the feasibility of theoretical results.
文摘The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.
