A novel planning tool for optimizing the placement of electric springs(ESs)in unbalanced distribution networks is introduced in this study.The total voltage deviation is used as the optimization criterion and is calcu...A novel planning tool for optimizing the placement of electric springs(ESs)in unbalanced distribution networks is introduced in this study.The total voltage deviation is used as the optimization criterion and is calculated when the ESs operate at their maximum reactive power either in the inductive or capacitive modes.The power rating of the ES is adjusted on the basis of the available active power at the bus.And in the optimization problem,it is expressed as the power ratio of the noncritical load(NCL)and critical load(CL).The implemented ES model is flexible,which can be used on any bus and any phase.The model determines the output voltage from the parameters and operating conditions at the point of common coupling(PCC).These conditions are integrated using the backward/forward sweep method(BFSM)and are updated during power flow calculations.The problem is described as a mixed-integer nonlinear problem and solved efficiently using an improved BFSM-based genetic algorithm,which computes power flow and ES placement simultaneously.The effectiveness of this method is evaluated through testing in IEEE 13-bus and 34-bus systems.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but t...The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but the control domain is not necessarily convex.展开更多
A detailed study of the mechanisms of the emissions of pions and protons in the forward and backward hemispheres in 4.5 A GeV/c oxygen-emulsion interactions has been carried out. The correlations between the multiplic...A detailed study of the mechanisms of the emissions of pions and protons in the forward and backward hemispheres in 4.5 A GeV/c oxygen-emulsion interactions has been carried out. The correlations between the multiplicities of secondary charged particles in the backward and forward hemispheres are investigated.展开更多
This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, th...This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments （MOM）. Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.展开更多
In this paper, a mathematical model consisting of forward and backward models is built on parallel genetic algorithms (PGAs) for fault diagnosis in a transmission power system. A new method to reduce the scale of faul...In this paper, a mathematical model consisting of forward and backward models is built on parallel genetic algorithms (PGAs) for fault diagnosis in a transmission power system. A new method to reduce the scale of fault sections is developed in the forward model and the message passing interface (MPI) approach is chosen to parallel the genetic algorithms by global sin-gle-population master-slave method (GPGAs). The proposed approach is applied to a sample system consisting of 28 sections, 84 protective relays and 40 circuit breakers. Simulation results show that the new model based on GPGAs can achieve very fast computation in online applications of large-scale power systems.展开更多
In this work, two types of predictability are proposed—forward and backward predictability—and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively est...In this work, two types of predictability are proposed—forward and backward predictability—and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively estimate the local forward and backward predictability limits of states in phase space. The forward predictability mainly focuses on the forward evolution of initial errors superposed on the initial state over time, while the backward predictability is mainly concerned with when the given state can be predicted before this state happens. From the results, there is a negative correlation between the local forward and backward predictability limits. That is, the forward predictability limits are higher when the backward predictability limits are lower, and vice versa. We also find that the sum of forward and backward predictability limits of each state tends to fluctuate around the average value of sums of the forward and backward predictability limits of sufficient states.Furthermore, the average value is constant when the states are sufficient. For different chaotic systems, the average value is dependent on the chaotic systems and more complex chaotic systems get a lower average value. For a single chaotic system,the average value depends on the magnitude of initial perturbations. The average values decrease as the magnitudes of initial perturbations increase.展开更多
The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also pr...The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved.展开更多
As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonh...As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonhomogeneous(H, Q) -process.展开更多
Based on the MAS rolling process in plate mill, the mathematical models of forward and backward slips of the wedges at plate head and tail were derived. According to the new model, the difference between the forward s...Based on the MAS rolling process in plate mill, the mathematical models of forward and backward slips of the wedges at plate head and tail were derived. According to the new model, the difference between the forward slip of the wedge and that of the normal part of the plate is obviously very small. The deviation is less than 2.5 % in general. Thus, in actual application, the forward slip of normal part of the plate can be used to calculate the length of rolled plate instead of the derived model. The rationality of this simplified method was confirmed with the application in Shougang 3 500 mm plate mill. The test results showed that the wedges of plate head and tail are symmetrical. The plate width deviation is greatly decreased by using the MAS method.展开更多
Forward and backward reaching inverse kinematics(FABRIK)is an efficient two-stage iterative solver for inverse kinematics of spherical-joint manipulator without the calculation of Jacobian matrix.Based on FABRIK,this ...Forward and backward reaching inverse kinematics(FABRIK)is an efficient two-stage iterative solver for inverse kinematics of spherical-joint manipulator without the calculation of Jacobian matrix.Based on FABRIK,this paper presents an incremental control scheme for a free-floating space manipulator consists of revolute joints and rigid links with the consideration of joint constraints and dynamic coupling effect.Due to the characteristics of FABRIK,it can induce large angular movements on specific joints.Apart from that,FABRIK maps three dimensional(3D)problem into two dimensional(2D)problem by a simple geometric projection.This operation can cause infinite loops in some cases.In order to overcome these issues and apply FABRIK on space manipulators,an increments allocation method is developed to constrain the angular movements as well as to re-orient the end-effector.The manipulator is re-positioned based on the momentum conservation law.Instead of pure target position tracking,the orientation control of the end-effector is also considered.Numerical simulation is performed to testify and demonstrate the effectiveness and reliability of the proposed incremental control approach.展开更多
A general type of forward-backward doubly stochastic differential equations （FBDSDEs） is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some...A general type of forward-backward doubly stochastic differential equations （FBDSDEs） is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a incthod of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.展开更多
This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information avail...This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.展开更多
The article first studies the fully coupled Forward-Backward Stochastic Differential Equations （FBSDEs） with the continuous local martingale. The article is mainly divided into two parts. In the first part, it consi...The article first studies the fully coupled Forward-Backward Stochastic Differential Equations （FBSDEs） with the continuous local martingale. The article is mainly divided into two parts. In the first part, it considers Backward Stochastic Differential Equations （BSDEs） with the continuous local martingale. Then, on the basis of it, in the second part it considers the fully coupled FBSDEs with the continuous local martingale. It is proved that their solutions exist and are unique under the monotonicity conditions.展开更多
In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedba...In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations.展开更多
In this paper, we propose a new second order numerical scheme for solving backward stochastic differential equations with jumps with the generator linearly depending on . And we theoretically prove that the conv...In this paper, we propose a new second order numerical scheme for solving backward stochastic differential equations with jumps with the generator linearly depending on . And we theoretically prove that the convergence rates of them are of second order for solving and of first order for solving and in norm.展开更多
In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The firs...In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.展开更多
基金supported by Consejo Nacional de Humanidades,Ciencia y Tecnología(CONAHCYT)—México(No.863547)the fellowship 2021-000001-01NACF-00604 given to the G.H.Valencia-Riverathe scholarships 175599,64698,253652,and 296574,given to G.Tapia-Tinoco,A.Garcia-Perez,D.Granados-Lieberman,and M.Valtierra-Rodriguez,respectively,through the Sistema Nacional de Investigadoras e Investigadores(SNII)-CONAHCYT-México.
文摘A novel planning tool for optimizing the placement of electric springs(ESs)in unbalanced distribution networks is introduced in this study.The total voltage deviation is used as the optimization criterion and is calculated when the ESs operate at their maximum reactive power either in the inductive or capacitive modes.The power rating of the ES is adjusted on the basis of the available active power at the bus.And in the optimization problem,it is expressed as the power ratio of the noncritical load(NCL)and critical load(CL).The implemented ES model is flexible,which can be used on any bus and any phase.The model determines the output voltage from the parameters and operating conditions at the point of common coupling(PCC).These conditions are integrated using the backward/forward sweep method(BFSM)and are updated during power flow calculations.The problem is described as a mixed-integer nonlinear problem and solved efficiently using an improved BFSM-based genetic algorithm,which computes power flow and ES placement simultaneously.The effectiveness of this method is evaluated through testing in IEEE 13-bus and 34-bus systems.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Supported by National Natural Science Foundation of P.R.China (10371067) the Youth Teacher Foundation of Fok Ying Tung Education Foundation (91064)New Century Excellent Young Teachers Foundation of P. R. China (NCEF-04-0633)
文摘The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but the control domain is not necessarily convex.
基金Project supported by the National Natural Science Foundation of China （Grant No 10475054）, the Major Science and Technology Foundation of Ministry of Education of China （Grant No 205026）, the Natural Science Foundation of Shanxi Province, China（Grant No 20021007） and Shanxi Provincial Foundation for Returned Scholars of China（Grant No 20031046）.
文摘A detailed study of the mechanisms of the emissions of pions and protons in the forward and backward hemispheres in 4.5 A GeV/c oxygen-emulsion interactions has been carried out. The correlations between the multiplicities of secondary charged particles in the backward and forward hemispheres are investigated.
基金Project supported by the National Natural Science Foundation of China (Grant No 60571058)the National Defense Foundation of China
文摘This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments （MOM）. Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.
基金the National Natural Science Foundation of China (No. 50677062)the New Century Excellent Talents in Uni-versity of China (No. NCET-07-0745)the Natural Science Foundation of Zhejiang Province, China (No. R107062)
文摘In this paper, a mathematical model consisting of forward and backward models is built on parallel genetic algorithms (PGAs) for fault diagnosis in a transmission power system. A new method to reduce the scale of fault sections is developed in the forward model and the message passing interface (MPI) approach is chosen to parallel the genetic algorithms by global sin-gle-population master-slave method (GPGAs). The proposed approach is applied to a sample system consisting of 28 sections, 84 protective relays and 40 circuit breakers. Simulation results show that the new model based on GPGAs can achieve very fast computation in online applications of large-scale power systems.
基金jointly supported by the National Natural Science Foundation of China for Excellent Young Scholars (Grant No. 41522502)the National Program on Global Change and Air–Sea Interaction (Grant Nos. GASI-IPOVAI06 and GASI-IPOVAI-03)the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2015BAC03B07)
文摘In this work, two types of predictability are proposed—forward and backward predictability—and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively estimate the local forward and backward predictability limits of states in phase space. The forward predictability mainly focuses on the forward evolution of initial errors superposed on the initial state over time, while the backward predictability is mainly concerned with when the given state can be predicted before this state happens. From the results, there is a negative correlation between the local forward and backward predictability limits. That is, the forward predictability limits are higher when the backward predictability limits are lower, and vice versa. We also find that the sum of forward and backward predictability limits of each state tends to fluctuate around the average value of sums of the forward and backward predictability limits of sufficient states.Furthermore, the average value is constant when the states are sufficient. For different chaotic systems, the average value is dependent on the chaotic systems and more complex chaotic systems get a lower average value. For a single chaotic system,the average value depends on the magnitude of initial perturbations. The average values decrease as the magnitudes of initial perturbations increase.
基金This work was supported by the National Natural Science Foundation of China (10001022 and 10371067)the Excellent Young Teachers Program and the Doctoral program Foundation of MOE and Shandong Province,P.R.C.
文摘The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved.
文摘As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonhomogeneous(H, Q) -process.
文摘Based on the MAS rolling process in plate mill, the mathematical models of forward and backward slips of the wedges at plate head and tail were derived. According to the new model, the difference between the forward slip of the wedge and that of the normal part of the plate is obviously very small. The deviation is less than 2.5 % in general. Thus, in actual application, the forward slip of normal part of the plate can be used to calculate the length of rolled plate instead of the derived model. The rationality of this simplified method was confirmed with the application in Shougang 3 500 mm plate mill. The test results showed that the wedges of plate head and tail are symmetrical. The plate width deviation is greatly decreased by using the MAS method.
基金supported by the National Natural Science Foundation of China(Nos.61803312,91848205 and 61725303).
文摘Forward and backward reaching inverse kinematics(FABRIK)is an efficient two-stage iterative solver for inverse kinematics of spherical-joint manipulator without the calculation of Jacobian matrix.Based on FABRIK,this paper presents an incremental control scheme for a free-floating space manipulator consists of revolute joints and rigid links with the consideration of joint constraints and dynamic coupling effect.Due to the characteristics of FABRIK,it can induce large angular movements on specific joints.Apart from that,FABRIK maps three dimensional(3D)problem into two dimensional(2D)problem by a simple geometric projection.This operation can cause infinite loops in some cases.In order to overcome these issues and apply FABRIK on space manipulators,an increments allocation method is developed to constrain the angular movements as well as to re-orient the end-effector.The manipulator is re-positioned based on the momentum conservation law.Instead of pure target position tracking,the orientation control of the end-effector is also considered.Numerical simulation is performed to testify and demonstrate the effectiveness and reliability of the proposed incremental control approach.
基金supported by the National Natural Science Foundation of China (No. 10771122)the NaturalScience Foundation of Shandong Province of China (No. Y2006A08)the National Basic ResearchProgram of China (973 Program) (No. 2007CB814900)
文摘A general type of forward-backward doubly stochastic differential equations （FBDSDEs） is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a incthod of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed.
文摘This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.
文摘The article first studies the fully coupled Forward-Backward Stochastic Differential Equations （FBSDEs） with the continuous local martingale. The article is mainly divided into two parts. In the first part, it considers Backward Stochastic Differential Equations （BSDEs） with the continuous local martingale. Then, on the basis of it, in the second part it considers the fully coupled FBSDEs with the continuous local martingale. It is proved that their solutions exist and are unique under the monotonicity conditions.
基金The NSF(10671112)of ChinaNational Basic Research Program(973 Program)(2007CB814904)of Chinathe NSF(Z2006A01)of Shandong Province and the Chinese New Century Young Teachers Program
文摘In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations.
文摘In this paper, we propose a new second order numerical scheme for solving backward stochastic differential equations with jumps with the generator linearly depending on . And we theoretically prove that the convergence rates of them are of second order for solving and of first order for solving and in norm.
基金supported in part by theNSFC(11871037)Shandong Province(JQ201202)+3 种基金NSFC-RS(11661130148NA150344)111 Project(B12023)supported by the Qingdao Postdoctoral Application Research Project(QDBSH20220202092)。
文摘In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.
