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Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps 被引量:2
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作者 Huai-Nian Zhu Cheng-Ke Zhang Ning Bin 《Applied Mathematics》 2012年第10期1321-1326,共6页
This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the ... This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the assumption of stochastic stabilizability, necessary and sufficient condition for the existence of the optimal control strategies is presented by means of a system of coupled algebraic Riccati equations via using the stochastic optimal control theory. Furthermore, the stochastic H∞ control problem for stochastic systems with Markovian jumps is discussed as an immediate application, and meanwhile, an illustrative example is presented. 展开更多
关键词 stochastic Systems differential gameS Markovian JUMPS stochastic H∞ Control
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Open Loop Saddle Point on Linear Quadratic Stochastic Differential Games
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作者 WANG JUN 《Communications in Mathematical Research》 CSCD 2014年第1期11-22,共12页
In this paper, we deal with one kind of two-player zero-sum linear quadratic stochastic differential game problem. We give the existence of an open loop saddle point if and only if the lower and upper values exist.
关键词 stochastic differential game saddle point open loop strategy
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Stochastic Differential Game Model for Decentralized Power Control with Wisdom Regulation Factor in Wearable Audio-Oriented BodyNets
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作者 Chen Yueyun Zhang Long Zhou Xianwei 《China Communications》 SCIE CSCD 2012年第12期117-126,共10页
In this study, aiming at the characteristics of randomness and dynamics in Wearable Audiooriented BodyNets (WA-BodyNets), stochastic differential game theory is applied to the investigation of the problem of transm... In this study, aiming at the characteristics of randomness and dynamics in Wearable Audiooriented BodyNets (WA-BodyNets), stochastic differential game theory is applied to the investigation of the problem of transmitted power control inconsumer electronic devices. First, astochastic differential game model is proposed for non-cooperative decentralized uplink power control with a wisdom regulation factor over WA-BodyNets with a onehop star topology.This model aims to minimize the cost associated with the novel payoff function of a player, for which two cost functions are defined: functions of inherent power radiation and accumulated power radiation darmge. Second, the feedback Nash equilibrium solution of the proposed model and the constraint of the Quality of Service (QoS) requirement of the player based on the SIR threshold are derived by solving the Fleming-Bellman-Isaacs partial differential equations. Furthermore, the Markov property of the optimal feedback strategies in this model is verified.The simulation results show that the proposed game model is effective and feasible for controlling the transmitted power of WA-BodyNets. 展开更多
关键词 stochastic differential game body area networks power control wisdom regulation factor
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Relationship between Maximum Principle and Dynamic Programming in Stochastic Differential Games and Applications
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作者 Jingtao Shi 《American Journal of Operations Research》 2013年第6期445-453,共9页
This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among... This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among the adjoint processes, the generalized Hamiltonian function and the value function are given. A portfolio optimization problem under model uncertainty in the financial market is discussed to show the applications of our result. 展开更多
关键词 stochastic Optimal Control stochastic differential gameS Dynamic PROGRAMMING MAXIMUM PRINCIPLE PORTFOLIO Optimization Model Uncertainty
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LINEAR QUADRATIC NONZERO-SUM DIFFERENTIAL GAMES WITH RANDOM JUMPS 被引量:3
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作者 吴臻 于志勇 《应用数学和力学》 CSCD 北大核心 2005年第8期945-950,共6页
The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Th... The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations. 展开更多
关键词 随机微分方程 泊松过程 随机微分对策
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LINEAR QUADRATIC NONZERO-SUM DIFFERENTIAL GAMES WITH RANDOM JUMPS 被引量:5
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作者 WU Zhen(吴臻) YU Zhi-yong(于志勇) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第8期1034-1039,共6页
The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. ... The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations. 展开更多
关键词 stochastic differential equation Poisson process stochastic differential game
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Linear Quadratic Leader-Follower Stochastic Differential Games:Closed-Loop Solvability
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作者 LI Zixuan SHI Jingtao 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2023年第4期1373-1406,共34页
In this paper,a leader-follower stochastic differential game is studied for a linear stochastic differential equation with quadratic cost functionals.The coefficients in the state equation and the weighting matrices i... In this paper,a leader-follower stochastic differential game is studied for a linear stochastic differential equation with quadratic cost functionals.The coefficients in the state equation and the weighting matrices in the cost functionals are all deterministic.Closed-loop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in applications.The follower first solves a stochastic linear quadratic optimal control problem,and his optimal closed-loop strategy is characterized by a Riccati equation,together with an adapted solution to a linear backward stochastic differential equation.Then the leader turns to solve a stochastic linear quadratic optimal control problem of a forward-backward stochastic differential equation,necessary conditions for the existence of the optimal closed-loop strategy for the leader is given by a Riccati equation.Some examples are also given. 展开更多
关键词 Backward stochastic differential equation closed-loop solvability leader-follower stochastic differential game linear quadratic control Riccati equation Stackelberg equilibrium
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A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H_2/H_∞ CONTROL WITH RANDOM JUMPS
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作者 张启侠 孙启良 《Acta Mathematica Scientia》 SCIE CSCD 2015年第2期348-358,共11页
A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary an... A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps. 展开更多
关键词 Nonzero-sum stochastic differential games maximum principle Poisson process stochastic H2/H∞ control forward backward stochastic differential equations
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H_∞ control for stochastic systems with time-delay
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作者 LiuYungang FangRui ZhangYun LiYanfang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第2期356-362,共7页
The H∞-control problem of stochastic systems with time-delay is considered. The sufficient conditions are obtained, under which there are always state-feedback control and dynamic output-feedback control so that the ... The H∞-control problem of stochastic systems with time-delay is considered. The sufficient conditions are obtained, under which there are always state-feedback control and dynamic output-feedback control so that the resulting closed-loop system is internaly stable and L2 input-output stable in the sense of expectation. Furthermore, the explicit formulas of both kinds of controls are derived. An example is included to illustrate the correctness of theoretic results. 展开更多
关键词 stochastic time-delay systems H∞-control differential game linear matrix inequality.
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FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES 被引量:13
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作者 WUZhen 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2005年第2期179-192,共14页
In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash ... In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system. 展开更多
关键词 stochastic differential equations stochastic optimal control riccatiequation nonzero sum stochastic differential game
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Infnite time horizon nonzero-sum linear quadratic stochastic differential games with state and control-dependent noise 被引量:2
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作者 Huainian ZHU Chengke ZHANG 《控制理论与应用(英文版)》 EI CSCD 2013年第4期629-633,共5页
This paper discusses the infinite time horizon nonzero-sum linear quadratic (LQ) differential games of stochastic systems governed by Itoe's equation with state and control-dependent noise. First, the nonzero-sum L... This paper discusses the infinite time horizon nonzero-sum linear quadratic (LQ) differential games of stochastic systems governed by Itoe's equation with state and control-dependent noise. First, the nonzero-sum LQ differential games are formulated by applying the results of stochastic LQ problems. Second, under the assumption of mean-square stabilizability of stochastic systems, necessary and sufficient conditions for the existence of the Nash strategy are presented by means of four coupled stochastic algebraic Riccati equations. Moreover, in order to demonstrate the usefulness of the obtained results, the stochastic H-two/H-infinity control with state, control and external disturbance-dependent noise is discussed as an immediate application. 展开更多
关键词 stochastic system differential games stochastic H-two/H-infinity control
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Infinite horizon linear quadratic differential games for discrete-time stochastic systems 被引量:2
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作者 Huiying SUN Liuyang JIANG Weihai ZHANG 《控制理论与应用(英文版)》 EI 2012年第3期391-396,共6页
This paper deals with the infinite horizon linear quadratic (LQ) differential games for discrete-time stochas- tic systems with both state and control dependent noise. The Popov-Belevitch-Hautus (PBH) criteria for... This paper deals with the infinite horizon linear quadratic (LQ) differential games for discrete-time stochas- tic systems with both state and control dependent noise. The Popov-Belevitch-Hautus (PBH) criteria for exact observability and exact detectability of discrete-time stochastic systems are presented. By means of them, we give the optimal strategies (Nash equilibrium strategies) and the optimal cost values for infinite horizon stochastic differential games. It indicates that the infinite horizon LQ stochastic differential gaines are associated with four coupled matrix-valued equations. Further- more, an iterative algorithm is proposed to solve the four coupled equations. Finally, an example is given to demonstrate our results. 展开更多
关键词 Discrete-time stochastic systems Exact observability Exact detectability differential games Nash equi-librium
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Linear-quadratic generalized Stackelberg games with jump-diffusion processes and related forward-backward stochastic differential equations 被引量:1
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作者 Na Li Jie Xiong Zhiyong Yu 《Science China Mathematics》 SCIE CSCD 2021年第9期2091-2116,共26页
A kind of linear-quadratic Stackelberg games with the multilevel hierarchy driven by both Brownian motion and Poisson processes is considered.The Stackelberg equilibrium is presented by linear forward-backward stochas... A kind of linear-quadratic Stackelberg games with the multilevel hierarchy driven by both Brownian motion and Poisson processes is considered.The Stackelberg equilibrium is presented by linear forward-backward stochastic differential equations(FBSDEs)with Poisson processes(FBSDEPs)in a closed form.By the continuity method,the unique solvability of FBSDEPs with a multilevel self-similar domination-monotonicity structure is obtained. 展开更多
关键词 Stackelberg game forward-backward stochastic differential equation stochastic optimal control linear-quadratic problem Poisson process
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Maximum Principle for Non-Zero Sum Stochastic Differential Game with Discrete and Distributed Delays 被引量:1
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作者 ZHANG Qixia 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2021年第2期572-587,共16页
This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays.Not only the state variable,but also control variables of players involv... This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays.Not only the state variable,but also control variables of players involve discrete and distributed delays.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,the author establishes a necessary maximum principle and a sufficient verification theorem.To explain theoretical results,the author applies them to a dynamic advertising game problem. 展开更多
关键词 Distributed delay generalized anticipated backward stochastic differential equations maximum principle Nash equilibrium point non-zero sum stochastic differential game
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A BSDE Approach to Stochastic Differential Games Involving Impulse Controls and HJBI Equation 被引量:1
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作者 ZHANG Liangquan 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2022年第3期766-801,共36页
This paper focuses on zero-sum stochastic differential games in the framework of forwardbackward stochastic differential equations on a finite time horizon with both players adopting impulse controls.By means of BSDE ... This paper focuses on zero-sum stochastic differential games in the framework of forwardbackward stochastic differential equations on a finite time horizon with both players adopting impulse controls.By means of BSDE methods,in particular that of the notion from Peng’s stochastic backward semigroups,the authors prove a dynamic programming principle for both the upper and the lower value functions of the game.The upper and the lower value functions are then shown to be the unique viscosity solutions of the Hamilton-Jacobi-Bellman-Isaacs equations with a double-obstacle.As a consequence,the uniqueness implies that the upper and lower value functions coincide and the game admits a value. 展开更多
关键词 Dynamic programming principle(DPP) forward-backward stochastic differential equations(FBSDEs) Hamilton-Jacobi-Bellman-Isaacs(HJBI) impulse control stochastic differential games value function viscosity solution
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Stochastic Differential Games with Reflection and Related Obstacle Problems for Isaacs Equations
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作者 Rainer BUCKDAHN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2011年第4期647-678,共32页
In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations (RBSDEs). We will establish the d... In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations (RBSDEs). We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bettman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSDEs being sharper than that in the paper of E1 Karoui, Kapoudjian, Pardoux, Peng and Quenez (1997), which turns out to be very useful because it allows us to estimate the LP-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle. 展开更多
关键词 stochastic differential games value function reflected backward stochastic differential equations dynamic programming principle Isaacs equations with obstacles viscosity solution
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BACKWARD LINEAR-QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO-SUM DIFFERENTIAL GAME PROBLEM WITH RANDOM JUMPS
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作者 Detao ZHANG 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2011年第4期647-662,共16页
This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic ... This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations.The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed.All these results develop those of Lim, Zhou(2001) and Yu,Ji(2008). 展开更多
关键词 Backward stochastic differential equations nonzero-sum differential game optimal con-trol poisson processes Riccati equation.
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Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games
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作者 Qingfeng ZHU Lijiao SU +3 位作者 Fuguo LIU Yufeng SHI Yong’ao SHEN Shuyang WANG 《Frontiers of Mathematics in China》 SCIE CSCD 2020年第6期1307-1326,共20页
We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal... We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal distribution,and the cost functional is also of mean-field type.It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions.We establish a necessary condition in the form of maximum principle and a verification theorem,which is a sufficient condition for Nash equilibrium point.We use the theoretical results to deal with a partial information linear-quadratic(LQ)game,and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation. 展开更多
关键词 Non-zero sum stochastic differential game mean field backward doubly stochastic differential equation(BDSDE) Nash equilibrium point maximum principle
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Policy Iteration Algorithms for Zero-Sum Stochastic Differential Games with Long-Run Average Payoff Criteria
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作者 JoséDaniel López-Barrientos 《Journal of the Operations Research Society of China》 EI 2014年第4期395-421,共27页
This paper studies the policy iteration algorithm(PIA)for zero-sum stochastic differential games with the basic long-run average criterion,as well as with its more selective version,the so-called bias criterion.The sy... This paper studies the policy iteration algorithm(PIA)for zero-sum stochastic differential games with the basic long-run average criterion,as well as with its more selective version,the so-called bias criterion.The system is assumed to be a nondegenerate diffusion.We use Lyapunov-like stability conditions that ensure the existence and boundedness of the solution to certain Poisson equation.We also ensure the convergence of a sequence of such solutions,of the corresponding sequence of policies,and,ultimately,of the PIA. 展开更多
关键词 Ergodic payoff criterion Zero-sum stochastic differential games Policy iteration algorithm Nondegenerate diffusions Poisson equation Schäl convergence Bias game
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随机博弈下的库存系统
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作者 孔德荣 《计算机应用文摘》 2024年第15期159-163,共5页
文章建立了一个随机微分博弈模型,模拟了2家寡头企业基于动态定价和库存控制的竞争。根据动态规划原理,博弈的上、下限值满足相关的HJB方程。该方程通常不易求得显示解,因此可构造离散时间受控马氏链来逼近值函数和最优控制。此外,文章... 文章建立了一个随机微分博弈模型,模拟了2家寡头企业基于动态定价和库存控制的竞争。根据动态规划原理,博弈的上、下限值满足相关的HJB方程。该方程通常不易求得显示解,因此可构造离散时间受控马氏链来逼近值函数和最优控制。此外,文章通过数值例子直观展示了结果,为库存管理实践提供了定量参考。 展开更多
关键词 库存系统 随机微分博弈 马氏链逼近
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