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 t...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.展开更多
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
文摘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.
