Science Letters:A minimax optimal control strategy for uncertain quasi-Hamiltonian systems  

作　　者：Yong WAN Zu-guang YIN Wei-qiu ZHU 

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

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2008年第7期950-954,共5页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：the National Natural Science Foundation of China (No. 10772159);the Specialized Research Fund for DoctorProgram of Higher Education of China (No. 20060335125) ;theNatural Science Foundation of Zhejiang Province (No. Y607087),China

摘　　要：A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control, the partially averaged Ito stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index, the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs （HJI） equation. Numerical results for a controlled and stochastically excited DulTlng oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control,the partially averaged It stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index,the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs(HJI) equation. Numerical results for a controlled and stochastically excited Duffing oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.

关 键 词：Nonlinear quasi-Hamiltonian system Minimax optimal control Stochastic excitation Uncertain disturbance Stochastic averaging Stochastic differential game 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]