Probability-weighted nonlinear stochastic optimal control strategy of quasi-integrable Hamiltonian systems with uncertain parameters

被引:3
|
作者
Gu, X. D. [1 ]
Zhu, W. Q. [1 ,2 ]
机构
[1] Northwestern Polytech Univ, Dept Engn Mech, Xian 710129, Peoples R China
[2] Zhejiang Univ, Dept Mech, State Key Lab Fluid Power Transmiss & Control, Hangzhou 310027, Zhejiang, Peoples R China
基金
中国国家自然科学基金;
关键词
integrable Hamiltonian system; stochastic averaging; stochastic control; stochastic dynamical programming principle; uncertainty of parameter; STABILIZATION; ROBUSTNESS;
D O I
10.1002/rnc.3251
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The nonlinear stochastic optimal control problem of quasi-integrable Hamiltonian systems with uncertain parameters is investigated. The uncertain parameters are described by using a random vector with probability density function. First, the partially averaged Ito stochastic differential equations are derived by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, the dynamical programming equation is established based on stochastic dynamical programming principle. By minimizing the dynamical programming equation with respect to control forces, the optimal control forces can be derived, which are functions of the uncertain parameters. The final optimal control forces are then determined by probability-weighted average of the obtained control forces with the probability density of the uncertain parameters as weighting function. The mean control effectiveness and mean control efficiency are used to evaluate the proposed control strategy. The robustness of the proposed control is measured by using the ratios of the variation coefficients of mean control effectiveness and mean control efficiency to the variation coefficients of uncertain parameters. Finally, two examples are given to illustrate the proposed control strategy and its effectiveness and robustness. Copyright (c) 2014 John Wiley & Sons, Ltd.
引用
收藏
页码:3086 / 3098
页数:13
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