A stochastic optimal timedelay control method for stochastically excited nonlinear systems was proposed based on the stochastic averaging method for timedelay systems and the stochastic dynamical programming principle. The stochastic optimal timedelay control problem of nonlinear systems was converted into another nontimedelay optimal control problem by using the stochastic averaging method for timedelay systems. The dynamical programming equation for the converted control problem was established based on the stochastic dynamical programming principle. The optimal control law was obtained from this equation,and the optimal active timedelay control law was obtained by the transformation of the present and past system states. The optimal semiactive timedelay control law was also obtained according to the Bingham model of MR dampers. An example of stochastically excited and controlled hysteretic column was given to illustrate the application and effectiveness of the proposed stochastic optimal timedelay control method.
应祖光,洪沁.一种基于随机平均的最优时滞控制方法[J].动力学与控制学报,2008,6(3):260~264; Ying Zuguang, Hong Qin. An optimal timedelay control method based on the stochastic averaging[J]. Journal of Dynamics and Control,2008,6(3):260-264.