Stochastic optimal vibration control of partially observable nonlinear quasi Hamiltonian systems with actuator saturation

An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First, a controlled partially observable nonlinear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged Itô stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle, respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control efficiency.

[1]  Robert J. Elliott,et al.  Classes of Nonlinear Partially Observable Stochastic Optimal Control Problems with Explicit Optimal Control Laws , 1998 .

[3]  Jian-Qiao Sun,et al.  Non-linear stochastic control via stationary response design , 2003 .

[4]  T. T. Soong,et al.  A STOCHASTIC OPTIMAL SEMI-ACTIVE CONTROL STRATEGY FOR ER/MR DAMPERS , 2003 .

[5]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[6]  X. Zhou,et al.  Stochastic Controls: Hamiltonian Systems and HJB Equations , 1999 .

[7]  Z. G. Ying,et al.  Nonlinear stochastic optimal control of partially observable linear structures , 2002 .

[8]  Alexander S. Bratus,et al.  Optimal Bounded Response Control for a Second-Order System Under a White-Noise Excitation , 2000 .

[9]  Optimal bounded control for minimizing the response of quasi-integrable Hamiltonian systems , 2004 .

[10]  Stochastic Optimal Bounded Control for a System With the Boltz Cost Function , 2000 .

[11]  Alexander S. Bratus,et al.  Optimal bounded control of steady-state random vibrations , 2000 .

[12]  A. Bratus,et al.  Bounded parametric control of random vibrations , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[13]  Weiqiu Zhu,et al.  Stochastic Averaging of Quasi-Integrable Hamiltonian Systems , 1997 .

[14]  R. Elliott,et al.  Certain nonlinear partially observable stochastic optimal control problems with explicit control laws equivalent to LEQG/LQG problems , 1997, IEEE Trans. Autom. Control..

[15]  Zuguang,et al.  Stochastic optimal control of hysteretic systems under externally and parametrically random excitations , 2003 .

[16]  Weiqiu Zhu,et al.  Optimal Bounded Control for Minimizing the Response of Quasi Non-Integrable Hamiltonian Systems , 2004 .

[17]  On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems , 2004, Journal of Zhejiang University. Science.

[18]  T. T. Soong,et al.  An Optimal Nonlinear Feedback Control Strategy for Randomly Excited Structural Systems , 2001 .

[19]  Z. G. Ying,et al.  Optimal nonlinear feedback control of quasi-Hamiltonian systems , 1999 .