In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a ...In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation.展开更多
Despite the intensive studies on neurons, the control mechanism in real interactions of neurons is still unclear. This paper presents an understanding of this kind of control mechanism, controlling a neuron by stimula...Despite the intensive studies on neurons, the control mechanism in real interactions of neurons is still unclear. This paper presents an understanding of this kind of control mechanism, controlling a neuron by stimulating another coupled neuron, with the uncertainties taken into consideration for both neurons. Two observers and a differentiator, which comprise the first-order low-pass filters, are first designed for estimating the uncertainties. Then, with the estimated values combined, a robust nonlinear controller with a saturation function is presented to track the desired membrane potential. Finally,two typical bursters of neurons with the desired membrane potentials are proposed in the simulation, and the numerical results show that they are tracked very well by the proposed controller.展开更多
Spectral abscissa(SA)is defined as the real part of the rightmost characteristic root(s)of a dynamical system,and it can be regarded as the decaying rate of the system,the smaller the better from the viewpoint of fast...Spectral abscissa(SA)is defined as the real part of the rightmost characteristic root(s)of a dynamical system,and it can be regarded as the decaying rate of the system,the smaller the better from the viewpoint of fast stabilization.Based on the Puiseux series expansion of complex-valued functions,this paper shows that the SA can be minimized within a given delay interval at values where the characteristic equation has repeated roots with multiplicity 2 or 3.Four sufficient conditions in terms of the partial derivatives of the characteristic function are established for testing whether the SA is minimized or not,and they can be tested directly and easily.展开更多
This paper studies the stabilization to an inverted pendulum under a delayed proportional-derivative-acceleration(PDA)feedback,which can be used to understand human balance in quiet standing.The closed-loop system is ...This paper studies the stabilization to an inverted pendulum under a delayed proportional-derivative-acceleration(PDA)feedback,which can be used to understand human balance in quiet standing.The closed-loop system is described by a neutral delay differential equation(NDDE).The optimal feedback gains(OFGs)that make the exponential decaying rate maximized are determined when the characteristic equation of the closed-loop has a repeated real root with multiplicity 4.Such a property is called multiplicity-induced dominancy of time-delay systems,and has been discussed intensively by many authors for retarded delay differential equations(RDDEs).This paper shows that multiplicity-induced dominancy can be achieved in NDDEs.In addition,the OFGs are delay-dependent,and decrease sharply to small numbers correspondingly as the delay increases from zero and varies slowly with respect to moderate delays.Thus,the inverted pendulum can be well-stabilized with moderate delays and relatively small feedback gains.The result might be understandable that the elderly with obvious response delays can be well-stabilized with a delayed PDA feedback controller.展开更多
Fractional differential equations are more and more used in modeling memory(history-dependent,nonlocal,or hereditary) phenomena.Conventional initial values of fractional differential equations are define at a point,...Fractional differential equations are more and more used in modeling memory(history-dependent,nonlocal,or hereditary) phenomena.Conventional initial values of fractional differential equations are define at a point,while recent works defin initial conditions over histories.We prove that the conventional initialization of fractional differential equations with a Riemann–Liouville derivative is wrong with a simple counter-example.The initial values were assumed to be arbitrarily given for a typical fractional differential equation,but we fin one of these values can only be zero.We show that fractional differential equations are of infinit dimensions,and the initial conditions,initial histories,are define as functions over intervals.We obtain the equivalent integral equation for Caputo case.With a simple fractional model of materials,we illustrate that the recovery behavior is correct with the initial creep history,but is wrong with initial values at the starting point of the recovery.We demonstrate the application of initial history by solving a forced fractional Lorenz system numerically.展开更多
Organic nitrogen(ON)compounds play a significant role in the light absorption of brown carbon and the formation of organic aerosols,however,the mixing state,secondary formation processes,and influencing factors of ON ...Organic nitrogen(ON)compounds play a significant role in the light absorption of brown carbon and the formation of organic aerosols,however,the mixing state,secondary formation processes,and influencing factors of ON compounds are still unclear.This paper reports on the mixing state of ON-containing particles based on measurements obtained using a highperformance single particle aerosol mass spectrometer in January 2020 in Guangzhou.The ON-containing particles accounted for 21% of the total detected single particles,and the particle count and number fraction of the ON-containing particles were two times higher at night than during the day.The prominent increase in the content of ON-containing particles with the enhancement of NO_xmainly occurred at night,and accompanied by high relative humidity and nitrate,which were associated with heterogeneous reactions between organics and gaseous NO_(x)and/or NO_(3)radical.The synchronous decreases in ON-containing particles and the mass absorption coefficient of water-soluble extracts at 365 nm in the afternoon may be associated with photo-bleaching of the ON species in the particles.In addition,the positive matrix factorization analysis found five factors dominated the formation processes of ON particles,and the nitrate factor(33%)mainly contributed to the production of ON particles at night.The results of this study provide unique insights into the mixing states and secondary formation processes of the ON-containing particles.展开更多
This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex- DDEs. These results not o...This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex- DDEs. These results not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. To validate the effectiveness of the proposed criteria, the stabilization problem of the extended time delay auto-synchronization (ETDAS) control and n time delay auto-synchronization (NTDAS) control are then further investigated, respectively. The numerical simulations are consistent with the above theoretical analysis.展开更多
High levels of fine particulate matter(PM_(2.5))is linked to poor air quality and premature deaths,so haze pollution deserves the attention of the world.As abundant inorganic components in PM_(2.5),ammonium nitrate(NH...High levels of fine particulate matter(PM_(2.5))is linked to poor air quality and premature deaths,so haze pollution deserves the attention of the world.As abundant inorganic components in PM_(2.5),ammonium nitrate(NH_(4)NO_(3))formation includes two processes,the diffusion process(molecule of ammonia and nitric acid move from gas phase to liquid phase)and the ionization process(subsequent dissociation to form ions).In this study,we discuss the impact of meteorological factors,emission sources,and gaseous precursors on NH4NO3 formation based on thermodynamic theory,and identify the dominant factors during clean periods and haze periods.Results show that aerosol liquid water content has a more significant effect on ammonium nitrate formation regardless of the severity of pollution.The dust source is dominant emission source in clean periods;while a combination of coal combustion and vehicle exhaust sources is more important in haze periods.And the control of ammonia emission is more effective in reducing the formation of ammonium nitrate.The findings of this work inform the design of effective strategies to control particulate matter pollution.展开更多
基金supported by the National Natural Science Foundation of China (Grant 11372354)the Fund of the State Key Lab of Mechanics and Control of Mechanical Structures (Grant MCMS-0116K01)
文摘In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation.
基金Project supported by the National Natural Science Foundation of China(No.11372354)the Jiangsu Innovation Program for Graduate Education(No.KYLX16 0308)
文摘Despite the intensive studies on neurons, the control mechanism in real interactions of neurons is still unclear. This paper presents an understanding of this kind of control mechanism, controlling a neuron by stimulating another coupled neuron, with the uncertainties taken into consideration for both neurons. Two observers and a differentiator, which comprise the first-order low-pass filters, are first designed for estimating the uncertainties. Then, with the estimated values combined, a robust nonlinear controller with a saturation function is presented to track the desired membrane potential. Finally,two typical bursters of neurons with the desired membrane potentials are proposed in the simulation, and the numerical results show that they are tracked very well by the proposed controller.
基金Project supported by the National Natural Science Foundation of China(No.12072370)。
文摘Spectral abscissa(SA)is defined as the real part of the rightmost characteristic root(s)of a dynamical system,and it can be regarded as the decaying rate of the system,the smaller the better from the viewpoint of fast stabilization.Based on the Puiseux series expansion of complex-valued functions,this paper shows that the SA can be minimized within a given delay interval at values where the characteristic equation has repeated roots with multiplicity 2 or 3.Four sufficient conditions in terms of the partial derivatives of the characteristic function are established for testing whether the SA is minimized or not,and they can be tested directly and easily.
基金supported by the National Natural Science Foundation of China(No.12072370)。
文摘This paper studies the stabilization to an inverted pendulum under a delayed proportional-derivative-acceleration(PDA)feedback,which can be used to understand human balance in quiet standing.The closed-loop system is described by a neutral delay differential equation(NDDE).The optimal feedback gains(OFGs)that make the exponential decaying rate maximized are determined when the characteristic equation of the closed-loop has a repeated real root with multiplicity 4.Such a property is called multiplicity-induced dominancy of time-delay systems,and has been discussed intensively by many authors for retarded delay differential equations(RDDEs).This paper shows that multiplicity-induced dominancy can be achieved in NDDEs.In addition,the OFGs are delay-dependent,and decrease sharply to small numbers correspondingly as the delay increases from zero and varies slowly with respect to moderate delays.Thus,the inverted pendulum can be well-stabilized with moderate delays and relatively small feedback gains.The result might be understandable that the elderly with obvious response delays can be well-stabilized with a delayed PDA feedback controller.
基金supported by the National Natural Science Foundation of China(Grants 11372354 and 10825207)
文摘Fractional differential equations are more and more used in modeling memory(history-dependent,nonlocal,or hereditary) phenomena.Conventional initial values of fractional differential equations are define at a point,while recent works defin initial conditions over histories.We prove that the conventional initialization of fractional differential equations with a Riemann–Liouville derivative is wrong with a simple counter-example.The initial values were assumed to be arbitrarily given for a typical fractional differential equation,but we fin one of these values can only be zero.We show that fractional differential equations are of infinit dimensions,and the initial conditions,initial histories,are define as functions over intervals.We obtain the equivalent integral equation for Caputo case.With a simple fractional model of materials,we illustrate that the recovery behavior is correct with the initial creep history,but is wrong with initial values at the starting point of the recovery.We demonstrate the application of initial history by solving a forced fractional Lorenz system numerically.
基金supported by the Key-Area Research and Development Program of Guangdong Province(No.2020B1111360001)the National Natural Science Foundation of China(Nos.41805093 and 41827804)+7 种基金the Natural Science Foundation of Guangdong Province(No.2021A1515011206)the GDAS’Project of Science and Technology Development(No.2021GDASYL-20210103058)the State Key Laboratory of Organic Geochemistry(No.SKLOG202105)Guangdong Foundation for Program of Science and Technology Research(No.2020B1212060053)the State Key Laboratory of Loess and Quaternary Geology,Institute of Earth Environment,CAS(No.SKLLQG2218)Guangdong Basic and Applied Basic Research Foundation(No.2022A1515012165)Scientific research special project of Pudong new district Ecological and Environmental Bureau(No.PDHJ20210008)the Shanghai Municipal Science and Technology Commission Natural Fund(No.20ZR1449700)。
文摘Organic nitrogen(ON)compounds play a significant role in the light absorption of brown carbon and the formation of organic aerosols,however,the mixing state,secondary formation processes,and influencing factors of ON compounds are still unclear.This paper reports on the mixing state of ON-containing particles based on measurements obtained using a highperformance single particle aerosol mass spectrometer in January 2020 in Guangzhou.The ON-containing particles accounted for 21% of the total detected single particles,and the particle count and number fraction of the ON-containing particles were two times higher at night than during the day.The prominent increase in the content of ON-containing particles with the enhancement of NO_xmainly occurred at night,and accompanied by high relative humidity and nitrate,which were associated with heterogeneous reactions between organics and gaseous NO_(x)and/or NO_(3)radical.The synchronous decreases in ON-containing particles and the mass absorption coefficient of water-soluble extracts at 365 nm in the afternoon may be associated with photo-bleaching of the ON species in the particles.In addition,the positive matrix factorization analysis found five factors dominated the formation processes of ON particles,and the nitrate factor(33%)mainly contributed to the production of ON particles at night.The results of this study provide unique insights into the mixing states and secondary formation processes of the ON-containing particles.
基金This work was supported by National'Science Foundation for Distinguished Young Scholars under Grant No. 10825207, and in part by Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant No. 200430.
文摘This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex- DDEs. These results not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. To validate the effectiveness of the proposed criteria, the stabilization problem of the extended time delay auto-synchronization (ETDAS) control and n time delay auto-synchronization (NTDAS) control are then further investigated, respectively. The numerical simulations are consistent with the above theoretical analysis.
基金the National Natural Science Foundation of China(No.42077191)the Fundamental Research Funds for the Central Universities(Nos.63213072,63213074)+1 种基金the GDAS’Project of Science and Technology Development(No.2021GDASYL-20210103058)the Guangdong Basic and Applied Basic Research Foundation(No.2022A1515012165),The Blue Sky Foundation.
文摘High levels of fine particulate matter(PM_(2.5))is linked to poor air quality and premature deaths,so haze pollution deserves the attention of the world.As abundant inorganic components in PM_(2.5),ammonium nitrate(NH_(4)NO_(3))formation includes two processes,the diffusion process(molecule of ammonia and nitric acid move from gas phase to liquid phase)and the ionization process(subsequent dissociation to form ions).In this study,we discuss the impact of meteorological factors,emission sources,and gaseous precursors on NH4NO3 formation based on thermodynamic theory,and identify the dominant factors during clean periods and haze periods.Results show that aerosol liquid water content has a more significant effect on ammonium nitrate formation regardless of the severity of pollution.The dust source is dominant emission source in clean periods;while a combination of coal combustion and vehicle exhaust sources is more important in haze periods.And the control of ammonia emission is more effective in reducing the formation of ammonium nitrate.The findings of this work inform the design of effective strategies to control particulate matter pollution.