基于随机平均的非线性随机最优控制  

An Nonlinear Stochastic Optimal Control Based on Stochastic Averaging

作　　者：应祖光[1] 郭涛[1] 

机构地区：[1]浙江大学力学系,杭州310027

出　　处：《噪声与振动控制》2008年第1期1-3,12,共4页Noise and Vibration Control

基　　金：浙江省自然科学基金资助项目(Y607087)

摘　　要：首先建立非线性随机系统的最优控制问题,并介绍通过随机平均法导出平均系统、再由随机动态规划原理确定控制律的平均系统的非线性随机最优控制方法。然后,对于非线性随机系统的动态规划方程,提出应用随机平均法简化该方程、从而得到最优平均控制律的方法,并证明该最优平均控制律等价于平均系统的最优控制律。最后用一个例子说明方法及等价性,并指出在一定条件下,最优平均控制律将是动态规划方程的精确解。The optimal control problem is firstly established for a nonlinear stochastic system. The nonlinear stochastic optimal control strategy for an averaged system is presented which derives the averaged system by using the stochastic averaging method and obtains the control law according to the stochastic dynamical programming principle. Then for the dynamical programming equation of the nonlinear stochastic system, an optimal averaging solution is proposed by using the stochastic averaging method to simplify the original dynamical programming equation, and the nonlinear stochastic optimal averaging control strategy is obtained. The optimal averaging control law is proved to be equal to the optimal control law for the averaged system. Finally, an example is given to illustrate the application of the proposed method and the equality between the two control laws. Under a certain condition, the optimal averaging control law is an exact solution to the dynamical programming equation.

关 键 词：振动与波 非线性随机系统 随机动态规划 随机平均法 最优控制律 

分 类 号：O321[理学—一般力学与力学基础]