An Nonlinear Stochastic Optimal Control Based on Stochastic Averaging
Guo Liang Tao · Noise and Vibration Control · 2008
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.