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
The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential...The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.展开更多
Based upon the theory of the nonlinear quadric two-person nonzero-sum differential game,the fact that the time-limited mixed H2/H∞ control problem can be turned into the problem of solving the state feedback Nash bal...Based upon the theory of the nonlinear quadric two-person nonzero-sum differential game,the fact that the time-limited mixed H2/H∞ control problem can be turned into the problem of solving the state feedback Nash balance point is mentioned. Upon this,a theorem about the solution of the state feedback control is given,the Lyapunov stabilization of the nonlinear system under this control is proved,too. At the same time,this solution is used to design the nonlinear H2/H∞ guidance law of the relative motion between the missile and the target in three-dimensional(3D) space. By solving two coupled Hamilton-Jacobi partial differential inequalities(HJPDI),a control with more robust stabilities and more robust performances is obtained. With different H∞ performance indexes,the correlative weighting factors of the control are analytically designed. At last,simulations under different robust performance indexes and under different initial conditions and under the cases of intercepting different maneuvering targets are carried out. All results indicate that the designed law is valid.展开更多
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
基金This work is supported by the National Natural Science Foundation (Grant No.10371067)the Youth Teacher Foundation of Fok Ying Tung Education Foundation, the Excellent Young Teachers Program and the Doctoral Program Foundation of MOE and Shandong Province, China.
文摘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.
基金Project supported by the 973 National Basic Research Program of China (No. 2007CB814904)the National Natural Science Foundations of China (No. 10921101)+2 种基金the Shandong Provincial Natural Science Foundation of China (No. 2008BS01024)the Science Fund for Distinguished Young Scholars of Shandong Province (No. JQ200801)the Shandong University Science Fund for Distinguished Young Scholars(No. 2009JQ004)
文摘The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.
基金Sponsored by the National Natural Science Foundation of China (Grant No.90716028)
文摘Based upon the theory of the nonlinear quadric two-person nonzero-sum differential game,the fact that the time-limited mixed H2/H∞ control problem can be turned into the problem of solving the state feedback Nash balance point is mentioned. Upon this,a theorem about the solution of the state feedback control is given,the Lyapunov stabilization of the nonlinear system under this control is proved,too. At the same time,this solution is used to design the nonlinear H2/H∞ guidance law of the relative motion between the missile and the target in three-dimensional(3D) space. By solving two coupled Hamilton-Jacobi partial differential inequalities(HJPDI),a control with more robust stabilities and more robust performances is obtained. With different H∞ performance indexes,the correlative weighting factors of the control are analytically designed. At last,simulations under different robust performance indexes and under different initial conditions and under the cases of intercepting different maneuvering targets are carried out. All results indicate that the designed law is valid.
基金supported by National Natural Science Foundation of China(10671112)National Basic Research Program of China(973 Program)(2007CB814904)the Natural Science Foundation of Shandong Province(Z2006A01)
文摘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).
