Sliding mode control(SMC) becomes a common tool in designing robust nonlinear control systems, due to its inherent characteristics such as insensitivity to system uncertainties and fast dynamic response.Two modes are ...Sliding mode control(SMC) becomes a common tool in designing robust nonlinear control systems, due to its inherent characteristics such as insensitivity to system uncertainties and fast dynamic response.Two modes are involved in the SMC operation, namely reaching mode and sliding mode.In the reaching mode, the system state is forced to reach the sliding surface in a finite time.The major drawback of the SMC approach is the occurrence of chattering in the sliding mode, which is undesirable in most applications.Generally, the trade-off between chattering reduction and fast reaching time must be considered in the conventional SMC design.This paper proposes SMC design with a novel reaching law called the exponential rate reaching law(ERRL) to reduce chattering, and the control structure of the converter is designed based on the multiinput SMC that is applied to a three-phase AC/DC power converter.The simulation and experimental results show the effectiveness of the proposed technique.展开更多
In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker...In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker-Planck-Boltzmann equation near Maxwellians if initial data satisfies some smallness in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2)∩L_(k)^(p)L_(T)^(∞)L_(v)^(2).The second part proves the global existence of the mild solutions to the Vlasov-Poisson-Fokker-Planck system in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2),and we also obtain the exponential time decay rates,which are different from the algebraic time decay rates of the Fokker-Planck-Boltzmann equation.Our analysis is based on Lk1LT∞Lv2function space introduced by Duan et al.(Comm Pure Appl Math,2021,74:932-1020),the L_(k)^(1)∩L_(k)^(p) approach developed by Duan et al.(SIAM J Math Anal,2024,56:762-800),and the coercivity property of the Fokker-Planck operator.However,it is worth pointing out that the L_(k)^(1)∩L_(k)^(p)approach is not required for the Vlasov-Poisson-Fokker-Planck system,due to the influence of the electric field term,which is different from the Fokker-Planck-Boltzmann equation in this paper and in the work of Duan et al.(SIAM J Math Anal,2024,56:762-800).展开更多
The initial exponential growth rate of an epidemic is an important measure of the severeness of the epidemic,and is also closely related to the basic reproduction number.Estimating the growth rate from the epidemic cu...The initial exponential growth rate of an epidemic is an important measure of the severeness of the epidemic,and is also closely related to the basic reproduction number.Estimating the growth rate from the epidemic curve can be a challenge,because of its decays with time.For fast epidemics,the estimation is subject to over-fitting due to the limited number of data points available,which also limits our choice of models for the epidemic curve.We discuss the estimation of the growth rate using maximum likelihood method and simple models.展开更多
A flexible structure consisting of a Euler-Bernoulli beam with co-located sensors and actuators is considered. The control is a shear force in proportion to velocity. It is known that uniform exponential stability can...A flexible structure consisting of a Euler-Bernoulli beam with co-located sensors and actuators is considered. The control is a shear force in proportion to velocity. It is known that uniform exponential stability can be achieved with velocity feedback. A sensitivity asymptotic analysis of the system's eigenvalues and eigenfunctions is set up. The authors prove that, for K-1 epsilon (0, + infinity), all of the generalized eigenvectors of A form a Riesz basis of H. It is also proved that the optimal exponential decay rate can be obtained from the spectrum of the system for 0 < K-1 < + infinity.展开更多
A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed （i.i.d.） random variables, that is max{ηi, 1 ≤ i ≤ n}. T...A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed （i.i.d.） random variables, that is max{ηi, 1 ≤ i ≤ n}. The approximating technique is used to obtain the fluid approximation for the queue length, workload and busy time processes. Furthermore, under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, we prove by the approximating technique that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate only for large N. Here the scaled processes include the queue length process, workload process and busy time process.展开更多
Quarantine is a crucial control measure in reducing imported COVID-19 cases and community transmissions.However,some quarantined COVID-19 patients may show symptoms after finishing quarantine due to a long median incu...Quarantine is a crucial control measure in reducing imported COVID-19 cases and community transmissions.However,some quarantined COVID-19 patients may show symptoms after finishing quarantine due to a long median incubation period,potentially causing community transmissions.To assess the recommended 14-day quarantine policy,we develop a formula to estimate the quarantine failure rate from the incubation period distribution and the epidemic curve.We found that the quarantine failure rate increases with the exponential growth rate of the epidemic curve.We apply our formula to United States,Canada,and Hubei Province,China.Before the lockdown of Wuhan City,the quarantine failure rate in Hubei Province is about 4.1%.If the epidemic curve flattens or slowly decreases,the failure rate is less than 2.8%.The failure rate in US may be as high as 8.3%-11.5%due to a shorter 10-day quarantine period,while the failure rate in Canada may be between 2.5%and 3.9%.A 21-day quarantine period may reduce the failure rate to 0.3%-0.5%.展开更多
In this paper, we pay attention to the time-decay rate of the viscous bipolar quantum hydrodynamic （QHD） models for semiconductors. By applying the entropy method, we prove that the solution of the viscous bipolar Q...In this paper, we pay attention to the time-decay rate of the viscous bipolar quantum hydrodynamic （QHD） models for semiconductors. By applying the entropy method, we prove that the solution of the viscous bipolar QHD models tends to the equilibrium state at an exponential decay rate for the multi-dimensional cases. The arguments is based on a series of a priori estimates.展开更多
A multi-class single server queue under non-preemptive static buffer priority （SBP） service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length ...A multi-class single server queue under non-preemptive static buffer priority （SBP） service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length and busy time processes. Furthermore, we prove that the convergence rate of the fluid approximation for the queue length and busy time processes is exponential for large N. Additionally, a sufficient condition for stability is obtained.展开更多
Presents information on singularly peturbed two-point boundary value problem of convection-diffusion type. Analysis of the problem; Details of an hp version finite element method on a strongly graded piecewise uniform...Presents information on singularly peturbed two-point boundary value problem of convection-diffusion type. Analysis of the problem; Details of an hp version finite element method on a strongly graded piecewise uniform mesh of Shiskin type; Convergence of the method with respect to the singular perturbation parameter.展开更多
We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the proce...We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξ n ) on ?+, and reproduce independently new particles according to a probability law p(ξ n ) on ?. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean E ξ Z(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.展开更多
In a C1 non-uniformly hyperbolic systems with limit domination, we consider the periodic measures that supported on the Pesin set and keep a distance at least 6 to a hyperbolic ergodic measure μ given before. And the...In a C1 non-uniformly hyperbolic systems with limit domination, we consider the periodic measures that supported on the Pesin set and keep a distance at least 6 to a hyperbolic ergodic measure μ given before. And then, we bound from top the exponential growth rate of such periodic measures by the supremum of measure theoretic entropy on a closed set.展开更多
Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic p...Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence fate are embodied by the queue length, workload, and busy time processes.展开更多
文摘Sliding mode control(SMC) becomes a common tool in designing robust nonlinear control systems, due to its inherent characteristics such as insensitivity to system uncertainties and fast dynamic response.Two modes are involved in the SMC operation, namely reaching mode and sliding mode.In the reaching mode, the system state is forced to reach the sliding surface in a finite time.The major drawback of the SMC approach is the occurrence of chattering in the sliding mode, which is undesirable in most applications.Generally, the trade-off between chattering reduction and fast reaching time must be considered in the conventional SMC design.This paper proposes SMC design with a novel reaching law called the exponential rate reaching law(ERRL) to reduce chattering, and the control structure of the converter is designed based on the multiinput SMC that is applied to a three-phase AC/DC power converter.The simulation and experimental results show the effectiveness of the proposed technique.
基金supported by the National Natural Science Foundation of China(11801285,12326337)。
文摘In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker-Planck-Boltzmann equation near Maxwellians if initial data satisfies some smallness in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2)∩L_(k)^(p)L_(T)^(∞)L_(v)^(2).The second part proves the global existence of the mild solutions to the Vlasov-Poisson-Fokker-Planck system in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2),and we also obtain the exponential time decay rates,which are different from the algebraic time decay rates of the Fokker-Planck-Boltzmann equation.Our analysis is based on Lk1LT∞Lv2function space introduced by Duan et al.(Comm Pure Appl Math,2021,74:932-1020),the L_(k)^(1)∩L_(k)^(p) approach developed by Duan et al.(SIAM J Math Anal,2024,56:762-800),and the coercivity property of the Fokker-Planck operator.However,it is worth pointing out that the L_(k)^(1)∩L_(k)^(p)approach is not required for the Vlasov-Poisson-Fokker-Planck system,due to the influence of the electric field term,which is different from the Fokker-Planck-Boltzmann equation in this paper and in the work of Duan et al.(SIAM J Math Anal,2024,56:762-800).
基金This research is partially supported by a Natural Sciences and Engineering Research Council Canada discovery grant,and National Natural Science Foundation of China(No.11771075).
文摘The initial exponential growth rate of an epidemic is an important measure of the severeness of the epidemic,and is also closely related to the basic reproduction number.Estimating the growth rate from the epidemic curve can be a challenge,because of its decays with time.For fast epidemics,the estimation is subject to over-fitting due to the limited number of data points available,which also limits our choice of models for the epidemic curve.We discuss the estimation of the growth rate using maximum likelihood method and simple models.
文摘A flexible structure consisting of a Euler-Bernoulli beam with co-located sensors and actuators is considered. The control is a shear force in proportion to velocity. It is known that uniform exponential stability can be achieved with velocity feedback. A sensitivity asymptotic analysis of the system's eigenvalues and eigenfunctions is set up. The authors prove that, for K-1 epsilon (0, + infinity), all of the generalized eigenvectors of A form a Riesz basis of H. It is also proved that the optimal exponential decay rate can be obtained from the spectrum of the system for 0 < K-1 < + infinity.
基金Supported by the National Natural Science Foundation of China (No. 10826047 and No.10901023)by the Fundamental Research Funds for the Central Universities under Contract BUPT2009RC0707
文摘A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed （i.i.d.） random variables, that is max{ηi, 1 ≤ i ≤ n}. The approximating technique is used to obtain the fluid approximation for the queue length, workload and busy time processes. Furthermore, under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, we prove by the approximating technique that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate only for large N. Here the scaled processes include the queue length process, workload process and busy time process.
基金This research is supported by National Natural Science Foundation of China(No.11771075)(ML)Natural Science Foundation of Shanghai,China(No.21ZR1401000)(ML)+4 种基金State Scholarship Fund of China(CSC No.201906635011)(ML)a Fundamental Research Grant for Chinese Universities(ML)Canadian Institutes of Health Research's Canadian 2019 COVID-19 Rapid Research Fund(JM)Michael Smith Foundation for Health Research's COVID-19 Research Response Fund(JM)a Natural Sciences and Engineering Research Council Canada Discovery Grant(JM).
文摘Quarantine is a crucial control measure in reducing imported COVID-19 cases and community transmissions.However,some quarantined COVID-19 patients may show symptoms after finishing quarantine due to a long median incubation period,potentially causing community transmissions.To assess the recommended 14-day quarantine policy,we develop a formula to estimate the quarantine failure rate from the incubation period distribution and the epidemic curve.We found that the quarantine failure rate increases with the exponential growth rate of the epidemic curve.We apply our formula to United States,Canada,and Hubei Province,China.Before the lockdown of Wuhan City,the quarantine failure rate in Hubei Province is about 4.1%.If the epidemic curve flattens or slowly decreases,the failure rate is less than 2.8%.The failure rate in US may be as high as 8.3%-11.5%due to a shorter 10-day quarantine period,while the failure rate in Canada may be between 2.5%and 3.9%.A 21-day quarantine period may reduce the failure rate to 0.3%-0.5%.
文摘In this paper, we pay attention to the time-decay rate of the viscous bipolar quantum hydrodynamic （QHD） models for semiconductors. By applying the entropy method, we prove that the solution of the viscous bipolar QHD models tends to the equilibrium state at an exponential decay rate for the multi-dimensional cases. The arguments is based on a series of a priori estimates.
基金Supported by National Natural Science Foundation of China(Grant No.10901023)the Fundamental Research Funds for the Central Universities(Grant Nos.BUPT2009RC0707 and BUPT2011RC0704)
文摘A multi-class single server queue under non-preemptive static buffer priority （SBP） service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length and busy time processes. Furthermore, we prove that the convergence rate of the fluid approximation for the queue length and busy time processes is exponential for large N. Additionally, a sufficient condition for stability is obtained.
基金the U.S. National Science Foundation through grants DMS-9626193, DMS-0074301, and INT-9605050.
文摘Presents information on singularly peturbed two-point boundary value problem of convection-diffusion type. Analysis of the problem; Details of an hp version finite element method on a strongly graded piecewise uniform mesh of Shiskin type; Convergence of the method with respect to the singular perturbation parameter.
基金the National Natural Sciente Foundation of China (Grant Nos. 10771021, 10471012)Scientific Research Foundation for Returned Scholars, Ministry of Education of China (Grant No. [2005]564)
文摘We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξ n ) on ?+, and reproduce independently new particles according to a probability law p(ξ n ) on ?. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean E ξ Z(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.
基金supported by National Natural Science Foundation of China (Grant Nos. 10671006)supported by National Natural Science Foundation of China (Grant Nos. 10671006, 10831003)+1 种基金National Basic Research Program of China (973 Program, 2006CB805903)supported by CAPES (Brazil)
文摘In a C1 non-uniformly hyperbolic systems with limit domination, we consider the periodic measures that supported on the Pesin set and keep a distance at least 6 to a hyperbolic ergodic measure μ given before. And then, we bound from top the exponential growth rate of such periodic measures by the supremum of measure theoretic entropy on a closed set.
文摘Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence fate are embodied by the queue length, workload, and busy time processes.
