In order to increase the efficiency and reliability of the dynamic analysis for flexible planar linkage containing the coupling of multi-energy domains, a method based on bond graph is introduced. From the viewpoint o...In order to increase the efficiency and reliability of the dynamic analysis for flexible planar linkage containing the coupling of multi-energy domains, a method based on bond graph is introduced. From the viewpoint of power conservation, the peculiar property of bond graph multiport element MTF is discussed. The procedure of modeling planar flexible muhibody mechanical systems by bond graphs and its dynamic principle are deseribed. To overcome the algebraic difficulty brought by differential causality anti nonlinear junction structure, the constraint forces at joints can be considered as unknown effort sources and added to the corresponding O-junctions of system bond graph model. As a result, the automatic modeling on a computer is realized. The validity of the procedure is illustrated by a practical example.展开更多
A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is ...A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is obtained so the three types kinematics singularities namely inverse, direct and combined types, can be identified with the physical meaning.Then based on the principle of virtual work, a methodology for driving the dynamical equations of motion is developed.Meanwhile the whole actuating torques, the torques caused by the gravity, the velocity and the acceleration are computed respectively in the numerical example. Results show that torque caused by the acceleration term is much bigger than the other two terms.This approach leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure when the principle of virtual work is applied to solving the inverse dynamical problem.展开更多
Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clar...Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic：liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liqUid coupling dynamics can be easily numerically modeled. Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures.展开更多
The formulation of multibody dynamics was studied based on variational principle. The body coonection matrix was introduced to define the connection configuration. The expression for the system kinematics was obtained...The formulation of multibody dynamics was studied based on variational principle. The body coonection matrix was introduced to define the connection configuration. The expression for the system kinematics was obtained by using the body connection matrix. From variational principle the general dynamical equations for multibody system were derived and the dynamical equations were given for multibody system subjected to the constraints.展开更多
Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This r...Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This review synthesizes the theoretical advancements,computational approaches,emerging challenges,and possible research directions in the field.Firstly,we briefly review the fundamental theory of continuous-time optimal control,including Pontryagin's maximum principle(PMP)and dynamic programming principle(DPP).Secondly,we present the foundational results in optimal impulse control,including necessary conditions and sufficient conditions.Thirdly,we systematize impulse game methodologies,from Nash equilibrium existence theory to the connection between Nash equilibrium and systems stability.Fourthly,we summarize the numerical algorithms including the intelligent computation approaches.Finally,we examine the new trends and challenges in theory and applications as well as computational considerations.展开更多
This paper investigates an international optimal investmentCconsumption problem under a random time horizon.The investor may allocate wealth between a domestic bond and an international real project with production ou...This paper investigates an international optimal investmentCconsumption problem under a random time horizon.The investor may allocate wealth between a domestic bond and an international real project with production output,whose price may exhibit discontinuities.The model incorporates the effects of taxation and exchange rate dynamics,where the exchange rate follows a stochastic differential equation with jump-diffusion.The investor’s objective is to maximize the utility of consumption and terminal wealth over an uncertain investment horizon.It is worth noting that,under our framework,the exit time is not assumed to be a stopping time.In particular,for the case of constant relative risk aversion(CRRA),we derive the optimal investment and consumption strategies by applying the separation method to solve the associated HamiltonCJacobiCBellman(HJB)equation.Moreover,several numerical examples are provided to illustrate the practical applicability of the proposed results.展开更多
We consider variations of the classical jeep problems： the optimal logistics for a caravan of jeeps which travel together in the desert. The main purpose is to arrange the travels for the one-way trip and the round t...We consider variations of the classical jeep problems： the optimal logistics for a caravan of jeeps which travel together in the desert. The main purpose is to arrange the travels for the one-way trip and the round trip of a caravan of jeeps so that the chief jeep visits the farthest destination. Based on the dynamic program principle, the maximum distances for the caravan when only part of the jeeps should return and when all drivers should return are obtained. Some related results such as the efficiency of the abandoned jeeps, and the advantages of more jeeps in the caravan are also presented.展开更多
The continuous reduction of electrolytes by Li metal leads to a poor lifespan of lithium metal batteries(LMBs). Low Coulombic efficiency(CE) and safety concern due to dendrite growth are the challenging issues for LMB...The continuous reduction of electrolytes by Li metal leads to a poor lifespan of lithium metal batteries(LMBs). Low Coulombic efficiency(CE) and safety concern due to dendrite growth are the challenging issues for LMB electrolyte design. Novel electrolytes such as highly concentrated electrolytes(HCEs) have been proposed for improving interphase stability. However, this strategy is currently limited for high cost due to the use of a large amount of lithium salts as well as their high viscosity, reduced ion mobility, and poor wettability. In this work, we propose a new type of electrolyte having a moderate concentration. The electrolyte has the advantage of HCEs as the anion is preferentially reduced to form inorganic solidelectrolyte-interphase(SEI). Such optimization has been confirmed through combined spectroscopic and electrochemical characterizations and supported with the first-principle molecular dynamics simulation. We have shown the intrinsic connections between solution structure and their electrochemical stability. The 2.0 M LiDFOB/PC electrolyte, as predicted by our characterizations and simulations, allows stable charge–discharge of LNMO|Li cells at 5C for more than 1500 cycles. The 2.0 M electrolyte generates a dense layer of SEI containing fluoro-oxoborates, Li_(3)BO_(3), LiF, Li_(2)CO_(3), and some organic species effectively passivating the lithium metal, as confirmed by electron microscopy, X-ray photoelectron spectroscopy,and solid-state nuclear magnetic resonance.展开更多
The optimal bounded control of stochastic-excited systems with Duhem hysteretic components for maximizing system reliability is investigated. The Duhem hysteretic force is transformed to energy-depending damping and s...The optimal bounded control of stochastic-excited systems with Duhem hysteretic components for maximizing system reliability is investigated. The Duhem hysteretic force is transformed to energy-depending damping and stiffness by the energy dissipation balance technique. The controlled system is transformed to the equivalent non- hysteretic system. Stochastic averaging is then implemented to obtain the It5 stochastic equation associated with the total energy of the vibrating system, appropriate for eval- uating system responses. Dynamical programming equations for maximizing system re- liability are formulated by the dynamical programming principle. The optimal bounded control is derived from the maximization condition in the dynamical programming equation. Finally, the conditional reliability function and mean time of first-passage failure of the optimal Duhem systems are numerically solved from the Kolmogorov equations. The proposed procedure is illustrated with a representative example.展开更多
We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, wher...We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.展开更多
To enhance the reliability of the stochastically excited structure,it is significant to study the problem of stochastic optimal control for minimizing first-passage failure.Combining the stochastic averaging method wi...To enhance the reliability of the stochastically excited structure,it is significant to study the problem of stochastic optimal control for minimizing first-passage failure.Combining the stochastic averaging method with dynamical programming principle,we study the optimal control for minimizing first-passage failure of multidegrees-of-freedom(MDoF)nonlinear oscillators under Gaussian white noise excitations.The equations of motion of the controlled system are reduced to time homogenous difusion processes by stochastic averaging.The optimal control law is determined by the dynamical programming equations and the control constraint.The backward Kolmogorov(BK)equation and the Pontryagin equation are established to obtain the conditional reliability function and mean first-passage time(MFPT)of the optimally controlled system,respectively.An example has shown that the proposed control strategy can increase the reliability and MFPT of the original system,and the mathematical treatment is also facilitated.展开更多
According to the definition of the new hypothetical states which have obvious physical significance and are termed as no-gravity static and accelerated states, a method for exact computation of the parallel robot＇s g...According to the definition of the new hypothetical states which have obvious physical significance and are termed as no-gravity static and accelerated states, a method for exact computation of the parallel robot＇s generalized inertia matrix is presented. Based on the matrix theory, the generalized inertia matrix of the parallel robot can be computed on the assumption that the robot is in these new hypothetical states respectively. The approach is demonstrated by the Delta robot as an example. Based on the principle of the virtual work, the inverse dynamics model of the robot is formulized after the kinematics analysis. Finally, a numerical example is given and the element distribution of the Delta robot＇s inertia matrix in the workspace is studied. The method has computationa＇, advantage of numerical accuracy for the Delta robot and can be parallelized easily.展开更多
A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations ...A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.展开更多
This paper investigates an optimal investment strategy on consumption and portfolio problem, in which the investor must withdraw funds continuously at a given rate. By analyzing the evolving process of wealth, we give...This paper investigates an optimal investment strategy on consumption and portfolio problem, in which the investor must withdraw funds continuously at a given rate. By analyzing the evolving process of wealth, we give the definition of safe-region for investment. Moreover, in order to obtain the target wealth as quickly as possible, using Bellman dynamic programming principle, we get the optimal investment strategy and corresponding necessary expected time. At last we give some numerical computations for a set of different parameters.展开更多
The higher-order attraction of pullback attractors for non-autonomous parabolic equations involving Grushin operators is considered. Firstly, the maximum principle is studied.Next, the higher-order integrability of th...The higher-order attraction of pullback attractors for non-autonomous parabolic equations involving Grushin operators is considered. Firstly, the maximum principle is studied.Next, the higher-order integrability of the difference of weak solutions is established. Finally,the higher-order attraction is proved.展开更多
Eugene Nida's Translation Theory has a profound influence both on global and Chinese translation circle.Although this theory is widely used,it also become a controversial topic in a certain extent.Through the movi...Eugene Nida's Translation Theory has a profound influence both on global and Chinese translation circle.Although this theory is widely used,it also become a controversial topic in a certain extent.Through the movie MuLAN and some applications in useful areas to discuss whether Nida's Translation Theory is still applicable within translating field.展开更多
The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The res...The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The result is applied to a cash flow valuation problem with terminal wealth constraint in a financial market. An explicit optimal strategy is obtained in this example.展开更多
This paper focuses on the McKean-Vlasov system's stochastic optimal control problem with Markov regime-switching.To this end,the authors establish a new It?'s formula using the linear derivative on the Wassers...This paper focuses on the McKean-Vlasov system's stochastic optimal control problem with Markov regime-switching.To this end,the authors establish a new It?'s formula using the linear derivative on the Wasserstein space.This formula enables us to derive the Hamilton-Jacobi-Bellman equation and verification theorems for Mc Kean-Vlasov optimal controls with regime-switching using dynamic programming.As concrete applications,the authors first study the McKean-Vlasov stochastic linear quadratic optimal control problem of the Markov regime-switching system,where all the coefficients can depend on the jump that switches among a finite number of states.Then,the authors represent the optimal control by four highly coupled Riccati equations.Besides,the authors revisit a continuous-time Markowitz mean-variance portfolio selection model(incomplete market)for a market consisting of one bank account and multiple stocks,in which the bank interest rate,the appreciation and volatility rates of the stocks are Markov-modulated.The mean-variance efficient portfolios can be derived explicitly in closed forms based on solutions of four Riccati equations.展开更多
We study a new class of two-player,zero-sum,deterministic differential games where each player uses both continuous and impulse controls in an infinite horizon with discounted payoff.We assume that the form and cost o...We study a new class of two-player,zero-sum,deterministic differential games where each player uses both continuous and impulse controls in an infinite horizon with discounted payoff.We assume that the form and cost of impulses depend on nonlinear functions and the state of the system,respectively.We use Bellman's dynamic programming principle(DPP)and viscosity solutions approach to show,for this class of games,the existence and uniqueness of a solution for the associated Hamilton-Jacobi-Bellman-Isaacs(HJBI)partial differential equations(PDEs).We then,under Isaacs'condition,deduce that the lower and upper value functions coincide,and we give a computational procedure with a numerical test for the game.展开更多
This paper concerns two-player zero-sum stochastic differential games with nonanticipative strategies against closed-loop controls in the case where the coefficients of mean-field stochastic differential equations and...This paper concerns two-player zero-sum stochastic differential games with nonanticipative strategies against closed-loop controls in the case where the coefficients of mean-field stochastic differential equations and cost functional depend on the joint distribution of the state and the control.In our game,both the(lower and upper)value functions and the(lower and upper)second-order Bellman–Isaacs equations are defined on the Wasserstein space P_(2)(R^(n))which is an infinite dimensional space.The dynamic programming principle for the value functions is proved.If the(upper and lower)value functions are smooth enough,we show that they are the classical solutions to the second-order Bellman–Isaacs equations.On the other hand,the classical solutions to the(upper and lower)Bellman–Isaacs equations are unique and coincide with the(upper and lower)value functions.As an illustrative application,the linear quadratic case is considered.Under the Isaacs condition,the explicit expressions of optimal closed-loop controls for both players are given.Finally,we introduce the intrinsic notion of viscosity solution of our second-order Bellman–Isaacs equations,and characterize the(upper and lower)value functions as their viscosity solutions.展开更多
文摘In order to increase the efficiency and reliability of the dynamic analysis for flexible planar linkage containing the coupling of multi-energy domains, a method based on bond graph is introduced. From the viewpoint of power conservation, the peculiar property of bond graph multiport element MTF is discussed. The procedure of modeling planar flexible muhibody mechanical systems by bond graphs and its dynamic principle are deseribed. To overcome the algebraic difficulty brought by differential causality anti nonlinear junction structure, the constraint forces at joints can be considered as unknown effort sources and added to the corresponding O-junctions of system bond graph model. As a result, the automatic modeling on a computer is realized. The validity of the procedure is illustrated by a practical example.
基金Supported by National Natural Science Foundation of China (No. 50375106) andKey Laboratory of Intelligent Manufacturing at Shantou University Grant (No. Imstu-2002-11).
文摘A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is obtained so the three types kinematics singularities namely inverse, direct and combined types, can be identified with the physical meaning.Then based on the principle of virtual work, a methodology for driving the dynamical equations of motion is developed.Meanwhile the whole actuating torques, the torques caused by the gravity, the velocity and the acceleration are computed respectively in the numerical example. Results show that torque caused by the acceleration term is much bigger than the other two terms.This approach leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure when the principle of virtual work is applied to solving the inverse dynamical problem.
基金supported by the National Natural Science Foundation of China(No.10272034)the Fundamental Research Funds for the Central Universities of China(No.HEUCF130205)
文摘Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic：liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liqUid coupling dynamics can be easily numerically modeled. Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures.
文摘The formulation of multibody dynamics was studied based on variational principle. The body coonection matrix was introduced to define the connection configuration. The expression for the system kinematics was obtained by using the body connection matrix. From variational principle the general dynamical equations for multibody system were derived and the dynamical equations were given for multibody system subjected to the constraints.
文摘Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This review synthesizes the theoretical advancements,computational approaches,emerging challenges,and possible research directions in the field.Firstly,we briefly review the fundamental theory of continuous-time optimal control,including Pontryagin's maximum principle(PMP)and dynamic programming principle(DPP).Secondly,we present the foundational results in optimal impulse control,including necessary conditions and sufficient conditions.Thirdly,we systematize impulse game methodologies,from Nash equilibrium existence theory to the connection between Nash equilibrium and systems stability.Fourthly,we summarize the numerical algorithms including the intelligent computation approaches.Finally,we examine the new trends and challenges in theory and applications as well as computational considerations.
基金Supported by the Shandong Provincial Natural Science Foundation(ZR2024MA095)Natural Science Foun-dation of China(12401583)Basic Research Program of Jiangsu(BK20240416).
文摘This paper investigates an international optimal investmentCconsumption problem under a random time horizon.The investor may allocate wealth between a domestic bond and an international real project with production output,whose price may exhibit discontinuities.The model incorporates the effects of taxation and exchange rate dynamics,where the exchange rate follows a stochastic differential equation with jump-diffusion.The investor’s objective is to maximize the utility of consumption and terminal wealth over an uncertain investment horizon.It is worth noting that,under our framework,the exit time is not assumed to be a stopping time.In particular,for the case of constant relative risk aversion(CRRA),we derive the optimal investment and consumption strategies by applying the separation method to solve the associated HamiltonCJacobiCBellman(HJB)equation.Moreover,several numerical examples are provided to illustrate the practical applicability of the proposed results.
基金partially Supported by National Natural Science Foundation of China(70571079,60534080)China Postdoctoral Science Foundation(20100471140)
文摘We consider variations of the classical jeep problems： the optimal logistics for a caravan of jeeps which travel together in the desert. The main purpose is to arrange the travels for the one-way trip and the round trip of a caravan of jeeps so that the chief jeep visits the farthest destination. Based on the dynamic program principle, the maximum distances for the caravan when only part of the jeeps should return and when all drivers should return are obtained. Some related results such as the efficiency of the abandoned jeeps, and the advantages of more jeeps in the caravan are also presented.
基金financial support from the National Natural Science Foundation of China (21922410)the Zhejiang Provincial Natural Science Foundation (R19B050003 and LQ21B030006)+2 种基金the Scientific Research Fund of Zhejiang Provincial Education Department (Y201839549)the Zhejiang University K.P. Chao’s High Technology Development Foundation (2018RC009)the Postdoctoral Science Foundation of Zhejiang Province (ZJ2020079)。
文摘The continuous reduction of electrolytes by Li metal leads to a poor lifespan of lithium metal batteries(LMBs). Low Coulombic efficiency(CE) and safety concern due to dendrite growth are the challenging issues for LMB electrolyte design. Novel electrolytes such as highly concentrated electrolytes(HCEs) have been proposed for improving interphase stability. However, this strategy is currently limited for high cost due to the use of a large amount of lithium salts as well as their high viscosity, reduced ion mobility, and poor wettability. In this work, we propose a new type of electrolyte having a moderate concentration. The electrolyte has the advantage of HCEs as the anion is preferentially reduced to form inorganic solidelectrolyte-interphase(SEI). Such optimization has been confirmed through combined spectroscopic and electrochemical characterizations and supported with the first-principle molecular dynamics simulation. We have shown the intrinsic connections between solution structure and their electrochemical stability. The 2.0 M LiDFOB/PC electrolyte, as predicted by our characterizations and simulations, allows stable charge–discharge of LNMO|Li cells at 5C for more than 1500 cycles. The 2.0 M electrolyte generates a dense layer of SEI containing fluoro-oxoborates, Li_(3)BO_(3), LiF, Li_(2)CO_(3), and some organic species effectively passivating the lithium metal, as confirmed by electron microscopy, X-ray photoelectron spectroscopy,and solid-state nuclear magnetic resonance.
基金supported by the National Natural Science Foundation of China(Nos.11202181 and11402258)the Special Fund for the Doctoral Program of Higher Education of China(No.20120101120171)
文摘The optimal bounded control of stochastic-excited systems with Duhem hysteretic components for maximizing system reliability is investigated. The Duhem hysteretic force is transformed to energy-depending damping and stiffness by the energy dissipation balance technique. The controlled system is transformed to the equivalent non- hysteretic system. Stochastic averaging is then implemented to obtain the It5 stochastic equation associated with the total energy of the vibrating system, appropriate for eval- uating system responses. Dynamical programming equations for maximizing system re- liability are formulated by the dynamical programming principle. The optimal bounded control is derived from the maximization condition in the dynamical programming equation. Finally, the conditional reliability function and mean time of first-passage failure of the optimal Duhem systems are numerically solved from the Kolmogorov equations. The proposed procedure is illustrated with a representative example.
基金supported by the NSF of China(11071144,11171187,11222110 and 71671104)Shandong Province(BS2011SF010,JQ201202)+4 种基金SRF for ROCS(SEM)Program for New Century Excellent Talents in University(NCET-12-0331)111 Project(B12023)the Ministry of Education of Humanities and Social Science Project(16YJA910003)Incubation Group Project of Financial Statistics and Risk Management of SDUFE
文摘We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.
基金the National Natural Science Foundation of China(Nos.11272201,11132007 and 10802030)
文摘To enhance the reliability of the stochastically excited structure,it is significant to study the problem of stochastic optimal control for minimizing first-passage failure.Combining the stochastic averaging method with dynamical programming principle,we study the optimal control for minimizing first-passage failure of multidegrees-of-freedom(MDoF)nonlinear oscillators under Gaussian white noise excitations.The equations of motion of the controlled system are reduced to time homogenous difusion processes by stochastic averaging.The optimal control law is determined by the dynamical programming equations and the control constraint.The backward Kolmogorov(BK)equation and the Pontryagin equation are established to obtain the conditional reliability function and mean first-passage time(MFPT)of the optimally controlled system,respectively.An example has shown that the proposed control strategy can increase the reliability and MFPT of the original system,and the mathematical treatment is also facilitated.
基金Supported by National Natural Science Foundation of China (No. 50375106) , the State Scholarship Fund (No. 2004812032) and Key Laboratory of Intelligent Manufacturing at Shantou University ( No. Imstu-2002-11).
文摘According to the definition of the new hypothetical states which have obvious physical significance and are termed as no-gravity static and accelerated states, a method for exact computation of the parallel robot＇s generalized inertia matrix is presented. Based on the matrix theory, the generalized inertia matrix of the parallel robot can be computed on the assumption that the robot is in these new hypothetical states respectively. The approach is demonstrated by the Delta robot as an example. Based on the principle of the virtual work, the inverse dynamics model of the robot is formulized after the kinematics analysis. Finally, a numerical example is given and the element distribution of the Delta robot＇s inertia matrix in the workspace is studied. The method has computationa＇, advantage of numerical accuracy for the Delta robot and can be parallelized easily.
基金supported by the National Natural Science Foundation of China (11072212,10932009)the Zhejiang Natural Science Foundation of China (7080070)
文摘A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.
文摘This paper investigates an optimal investment strategy on consumption and portfolio problem, in which the investor must withdraw funds continuously at a given rate. By analyzing the evolving process of wealth, we give the definition of safe-region for investment. Moreover, in order to obtain the target wealth as quickly as possible, using Bellman dynamic programming principle, we get the optimal investment strategy and corresponding necessary expected time. At last we give some numerical computations for a set of different parameters.
基金Supported by Tian Yuan Fund of Mathematics(Grant No.11326100)the Natural Science Fundation of Gansu Province(Grant No.145RJZA033)
文摘The higher-order attraction of pullback attractors for non-autonomous parabolic equations involving Grushin operators is considered. Firstly, the maximum principle is studied.Next, the higher-order integrability of the difference of weak solutions is established. Finally,the higher-order attraction is proved.
文摘Eugene Nida's Translation Theory has a profound influence both on global and Chinese translation circle.Although this theory is widely used,it also become a controversial topic in a certain extent.Through the movie MuLAN and some applications in useful areas to discuss whether Nida's Translation Theory is still applicable within translating field.
基金supported by the National Natural Science Foundation of China(No.61573217)the 111 Project(No.B12023)the National High-level Personnel of Special Support Program and the Chang Jiang Scholar Program of the Ministry of Education of China
文摘The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The result is applied to a cash flow valuation problem with terminal wealth constraint in a financial market. An explicit optimal strategy is obtained in this example.
基金supported partly by the National Nature Science Foundation of China under Grant Nos.12171053,11701040,11871010,61871058the Fundamental Research Funds for the Central Universities of Renmin University of China under Grant No.23XNKJ05the Hong Kong General Research Fund under Grant Nos.15216720,15221621 and 15226922。
文摘This paper focuses on the McKean-Vlasov system's stochastic optimal control problem with Markov regime-switching.To this end,the authors establish a new It?'s formula using the linear derivative on the Wasserstein space.This formula enables us to derive the Hamilton-Jacobi-Bellman equation and verification theorems for Mc Kean-Vlasov optimal controls with regime-switching using dynamic programming.As concrete applications,the authors first study the McKean-Vlasov stochastic linear quadratic optimal control problem of the Markov regime-switching system,where all the coefficients can depend on the jump that switches among a finite number of states.Then,the authors represent the optimal control by four highly coupled Riccati equations.Besides,the authors revisit a continuous-time Markowitz mean-variance portfolio selection model(incomplete market)for a market consisting of one bank account and multiple stocks,in which the bank interest rate,the appreciation and volatility rates of the stocks are Markov-modulated.The mean-variance efficient portfolios can be derived explicitly in closed forms based on solutions of four Riccati equations.
基金supported by the National Center for Scientific and Technical Research CNRST,Rabat,Morocco[grant number 17 UIZ 19].
文摘We study a new class of two-player,zero-sum,deterministic differential games where each player uses both continuous and impulse controls in an infinite horizon with discounted payoff.We assume that the form and cost of impulses depend on nonlinear functions and the state of the system,respectively.We use Bellman's dynamic programming principle(DPP)and viscosity solutions approach to show,for this class of games,the existence and uniqueness of a solution for the associated Hamilton-Jacobi-Bellman-Isaacs(HJBI)partial differential equations(PDEs).We then,under Isaacs'condition,deduce that the lower and upper value functions coincide,and we give a computational procedure with a numerical test for the game.
基金supported by Natural Science Foundation of Shandong Province(Grant Nos.ZR2020MA032,ZR2022MA029)National Natural Science Foundation of China(Grant Nos.12171279,72171133)+1 种基金The second named author was supported by National Key R&D Program of China(Grant No.2022YFA1006102)National Natural Science Foundation of China(Grant No.11831010)。
文摘This paper concerns two-player zero-sum stochastic differential games with nonanticipative strategies against closed-loop controls in the case where the coefficients of mean-field stochastic differential equations and cost functional depend on the joint distribution of the state and the control.In our game,both the(lower and upper)value functions and the(lower and upper)second-order Bellman–Isaacs equations are defined on the Wasserstein space P_(2)(R^(n))which is an infinite dimensional space.The dynamic programming principle for the value functions is proved.If the(upper and lower)value functions are smooth enough,we show that they are the classical solutions to the second-order Bellman–Isaacs equations.On the other hand,the classical solutions to the(upper and lower)Bellman–Isaacs equations are unique and coincide with the(upper and lower)value functions.As an illustrative application,the linear quadratic case is considered.Under the Isaacs condition,the explicit expressions of optimal closed-loop controls for both players are given.Finally,we introduce the intrinsic notion of viscosity solution of our second-order Bellman–Isaacs equations,and characterize the(upper and lower)value functions as their viscosity solutions.
