Optimal bounded control of stochastically excited strongly nonlinear vibro-impact system
Optimal bounded control of stochastically excited strongly nonlinear vibro-impact system
复制标题
随机激励强非线性振动冲击系统的最优有界控制
DOI：
10.1177/1077546320929898
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发表时间：
2020-05
影响因子：
2.8
通讯作者：
Hu Rongchun
中科院分区：
文献类型：
--
作者：
Gu Xudong;Deng Zichen;Hu Rongchun
针对具有执行器饱和的随机激励下的强非线性冲击振动系统，提出了一种最优有界控制策略。首先，利用非光滑变换将冲击效应纳入等效方程。在轻阻尼和弱随机扰动的假设下，系统能量是一个缓慢变化的过程。利用强非线性系统包络线的随机平均，可以得到系统能量的部分平均Itô随机微分方程。将最优控制问题由原来的状态变量最优控制问题转化为等效的系统能量最优控制问题，降低了最优控制问题的维数。然后，根据随机极大值原理，建立了伴随变量的伴随方程和部分平均控制问题的极大值条件。对于无限时间区间遍历控制，假设伴随变量为平稳过程，并进一步简化伴随方程。最后，通过计算相关的Fokker-Plank-Kolmogorov方程，导出了系统能量的概率密度函数和最优控制系统的其他统计量。为了进行比较，还研究了砰砰控制，并对控制结果进行了比较，以显示所开发的控制策略的优势。
An optimal bounded control strategy for strongly nonlinear vibro-impact systems under stochastic excitations with actuator saturation is proposed. First, the impact effect is incorporated in an equivalent equation by using a nonsmooth transformation. Under the assumption of light damping and weak random perturbation, the system energy is a slowly varying process. By using the stochastic averaging of envelope for strongly nonlinear systems, the partially averaged Itô stochastic differential equation for system energy can be derived. The optimal control problem is transformed from the original optimal control problem for the state variables to an equivalent optimal control problem for the system energy, which decreases the dimensions of the optimal control problem. Then, based on stochastic maximum principle, an adjoint equation for the adjoint variable and the maximum condition of partially averaged control problem are established. For infinite time-interval ergodic control, the adjoint variable is assumed to be a stationary process and the adjoint equation can be further simplified. Finally, the probability density function of the system energy and other statistics of the optimally controlled system are derived by calculating the associated Fokker–Plank–Kolmogorov equation. For comparison, the bang–bang control is also investigated and the control results are compared to show the advantages of the developed control strategy.
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影响因子：
2.6
作者：
M. Dimentberg;D. Iourtchenko
通讯作者：
M. Dimentberg;D. Iourtchenko
影响因子：
2.2
作者：
H. Kushner
通讯作者：
H. Kushner
有界噪声扰动下振动冲击系统的混沌动力学
影响因子：
7.8
作者：
Jinqian Feng;Junli Liu
通讯作者：
Junli Liu
DOI：
10.1061/(asce)0733-9399(1991)117:8(1890
发表时间：
1991-08
期刊：
Journal of Engineering Mechanics-asce
影响因子：
--
作者：
W. Zhu;Y. Lin
通讯作者：
W. Zhu;Y. Lin
影响因子：
2.7
作者：
V. Babitsky
通讯作者：
V. Babitsky