| STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS~ |
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| 作者姓名： | DengMaolin HongMingchao ZhuWeiqiu |
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| 作者单位： | [1]DepartmentofBiomedicalEngineering,ZhejiangUniversity,Hangzhou310027,China [2]CenterofComputation,ZhejiangUniversity,Hangzhou310027,China [3]DepartmentofMechanics,ZhejiangUniversity,Hangzhou310027,China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China(No.19972059). |
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| 摘 要： | A strategy is proposed based on the stochastic averaging method for quasi nonintegrable Hamiltonian systems and the stochastic dynamical programming principle. The proposed strategy can be used to design nonlinear stochastic optimal control to minimize the response of quasi non-integrable Hamiltonian systems subject to Gaussian white noise excitation. By using the stochastic averaging method for quasi non-integrable Hamiltonian systems the equations of motion of a controlled quasi non-integrable Hamiltonian system is reduced to a one-dimensional averaged Ito stochastic differential equation. By using the stochastic dynamical programming principle the dynamical programming equation for minimizing the response of the system is formulated.The optimal control law is derived from the dynamical programming equation and the bounded control constraints. The response of optimally controlled systems is predicted through solving the FPK equation associated with It5 stochastic differential equation. An example is worked out in detail to illustrate the application of the control strategy proposed.
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| 关 键 词： | 准不完整哈密顿体系 最佳控制 随机平均理论 动态过程 线性二次高斯控制 |
| 收稿时间： | 28 October 2002 |
STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS |
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| DengMaolin HongMingchao ZhuWeiqiu.STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS~[J].Acta Mechanica Solida Sinica,2003,16(4):313-320. |
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| Authors: | Deng Maolin |
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| Institution: | (1) Department of Biomedical Engineering, Zhejiang University, 310027 Hangzhou, China;(2) Center of Computation, Zhejiang University, 310027 Hangzhou, China;(3) Department of Mechanics, Zhejiang University, 310027 Hangzhou, China |
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| Abstract: | A strategy is proposed based on the stochastic averaging method for quasi non- integrable Hamiltonian systems and the stochastic dynamical programming principle.The pro- posed strategy can be used to design nonlinear stochastic optimal control to minimize the response of quasi non-integrable Hamiltonian systems subject to Gaussian white noise excitation.By using the stochastic averaging method for quasi non-integrable Hamiltonian systems the equations of motion of a controlled quasi non-integrable Hamiltonian system is reduced to a one-dimensional av- eraged It stochastic differential equation.By using the stochastic dynamical programming princi- ple the dynamical programming equation for minimizing the response of the system is formulated. The optimal control law is derived from the dynamical programming equation and the bounded control constraints.The response of optimally controlled systems is predicted through solving the FPK equation associated with It stochastic differential equation.An example is worked out in detail to illustrate the application of the control strategy proposed. |
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| Keywords: | quasi non-integrable Hamiltonian system response optimal control stochastic averaging method dynamical programming |
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