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Optimal control strategies for stochastically excited quasi partially integrable Hamiltonian systems

ISSN号：0567-7718
期刊名称：《力学学报：英文版》
时间：0
分类：O3[理学—力学]
作者机构：[1]Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University,Hangzhou 310027, China
相关基金：The project supported by the National Natural Science Foundation of China （10332030） and Research Fund for Doctoral Program of Higher Education of China （20060335125）.

作者： Ronghua Huan Maolin Deng Weiqiu Zhu[1]

关键词：非线性系统, 哈密顿系统, 最佳控制状态, 动力学, Nonlinear system , Stochastic excitation Stochastic averaging , Optimal control , Dynamical programming

中文摘要：

在二不同控制策略设计了部分减轻伪的反应的这篇论文，受到随机的刺激的 integrable Hamiltonian 系统被建议。首先，由部分为伪使用随机的平均方法 integrable Hamiltonian 系统， n-DOF 部分控制了伪有随机的刺激的 integrable Hamiltonian 系统被变换成一套部分平均的 Itô 随机的微分方程。然后，与部分平均的 Itô 方程联系的动态编程方程被使用随机的动态编程原则提出。在第一控制策略，没有解决动态编程方程，最佳的控制法律从动态编程方程和控制限制被导出。在第二控制策略，最佳的控制法律被解决动态编程方程获得。最后，两回答控制，不受管束的系统通过解决与充分平均的 Itô 方程联系的 Fokker-Plank-Kolmogorov 方程被预言。一个例子被得出说明应用程序，二的有效性建议了控制策略。

英文摘要：

In this paper two different control strategies designed to alleviate the response of quasi partially integrable Hamiltonian systems subjected to stochastic excitation are proposed. First, by using the stochastic averaging method for quasi partially integrable Hamiltonian systems, an n-DOF controlled quasi partially integrable Hamiltonian system with stochastic excitation is converted into a set of partially averaged It^↑o stochastic differential equations. Then, the dynamical programming equation associated with the partially averaged It^↑o equations is formulated by applying the stochastic dynamical programming principle. In the first control strategy, the optimal control law is derived from the dynamical programming equation and the control constraints without solving the dynamical programming equation. In the second control strategy, the optimal control law is obtained by solving the dynamical programming equation. Finally, both the responses of controlled and uncontrolled systems are predicted through solving the Fokker-Plank-Kolmogorov equation associated with fully averaged It^↑o equations. An example is worked out to illustrate the application and effectiveness of the two proposed control strategies.

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