Stochastic optimal control of cable vibration in plane by using axial support motion  

作　　者：Ming Zhao Wei-Qiu Zhu 

机构地区：[1]Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, 310027 Hangzhou, China

出　　处：《Acta Mechanica Sinica》2011年第4期578-586,共9页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (11072212,10932009);the Zhejiang Natural Science Foundation of China (7080070)

摘　　要：A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.

关 键 词：Stay cable Active control - Stochastic optimalcontrol Dynamical programming principle 

分 类 号：O211.6[理学—概率论与数理统计] U653.928.1[理学—数学]