具有噪声观测的不确定非线性拟哈密顿系统的随机极大极小振动控制

IF 0.8 4区 工程技术 Q4 ACOUSTICS International Journal of Acoustics and Vibration Pub Date : 2019-12-31 DOI:10.20855/ijav.2019.24.41446
Z. Ying, R. Hu, R. Huan
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引用次数: 0

摘要

基于扩展卡尔曼滤波器和极大极小随机动力学规划原理,针对随机激励下具有噪声观测的不确定非线性拟哈密顿系统,提出了一种随机极小极大控制策略。将具有智能传感器和执行器的结构系统建模为具有噪声观测的受控、激励和耗散哈密顿系统。首先给出了随机激励下具有控制和观测的不确定非线性拟哈密顿系统的微分方程。从具有噪声观测的不确定拟哈密顿系统出发,得到了具有不确定参数的估计非线性随机控制系统。在这种情况下,通过基于扩展卡尔曼滤波器的观测来确定最佳估计状态。基于极大极小随机动态规划原理,得到了被估计不确定系统的对偶动态规划方程。针对有界不确定参数确定最坏情况下的扰动,并通过规划方程确定最坏情形下的最优控制律。将所提出的极小极大控制策略应用于两个具有控制和噪声观测的不确定非线性随机系统。数值结果说明了系统随机振动响应降低的控制有效性。所提出的极大极小控制策略适用于随机激励下具有噪声观测的一般不确定非线性多自由度结构系统。
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Stochastic Minimax Vibration Control for Uncertain Nonlinear Quasi-Hamiltonian Systems with Noisy Observations
A stochastic minimax control strategy for uncertain nonlinear quasi-Hamiltonian systems with noisy observations under random excitations is proposed based on the extended Kalman filter and minimax stochastic dynamical programming principle. A structure system with smart sensors and actuators is modeled as a controlled, excited and dissipative Hamiltonian system with noisy observations. The differential equations for the uncertain nonlinear quasi-Hamiltonian system with control and observation under random excitation are given first. The estimated nonlinear stochastic control system with uncertain parameters is obtained from the uncertain quasi-Hamiltonian system with noisy observation. In this case, the optimally estimated state is determined by the observation based on the extended Kalman filter. The dual dynamical programming equation for the estimated uncertain system is then obtained based on the minimax stochastic dynamical programming principle. The worst-case disturbances are determined for bounded uncertain parameters and the optimal control law is determined for the worst case by the programming equation. The proposed minimax control strategy is applied to two uncertain nonlinear stochastic systems with controls and noisy observations. The control effectiveness for the stochastic vibration response reductions of the systems is illustrated with numerical results. The proposed minimax control strategy is applicable to general uncertain nonlinear multi-degree-of-freedom structure systems with noisy observations under random excitations.
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来源期刊
International Journal of Acoustics and Vibration
International Journal of Acoustics and Vibration ACOUSTICS-ENGINEERING, MECHANICAL
CiteScore
1.60
自引率
10.00%
发文量
0
审稿时长
12 months
期刊介绍: The International Journal of Acoustics and Vibration (IJAV) is the refereed open-access journal of the International Institute of Acoustics and Vibration (IIAV). The IIAV is a non-profit international scientific society founded in 1995. The primary objective of the Institute is to advance the science of acoustics and vibration by creating an international organization that is responsive to the needs of scientists and engineers concerned with acoustics and vibration problems all around the world. Manuscripts of articles, technical notes and letters-to-the-editor should be submitted to the Editor-in-Chief via the on-line submission system. Authors wishing to submit an article need to log in on the IJAV website first. Users logged into the website are able to submit new articles, track the status of their articles already submitted, upload revised articles, responses and/or rebuttals to reviewers, figures, biographies, photographs, copyright transfer agreements, and send comments to the editor. Each time the status of an article submitted changes, the author will also be notified automatically by email. IIAV members (in good standing for at least six months) can publish in IJAV free of charge and their papers will be displayed on-line immediately after they have been edited and laid-out. Non-IIAV members will be required to pay a mandatory Article Processing Charge (APC) of $200 USD if the manuscript is accepted for publication after review. The APC fee allows IIAV to make your research freely available to all readers using the Open Access model. In addition, Non-IIAV members who pay an extra voluntary publication fee (EVPF) of $500 USD will be granted expedited publication in the IJAV Journal and their papers can be displayed on the Internet after acceptance. If the $200 USD (APC) publication fee is not honored, papers will not be published. Authors who do not pay the voluntary fixed fee of $500 USD will have their papers published but there may be a considerable delay. The English text of the papers must be of high quality. If the text submitted is of low quality the manuscript will be more than likely rejected. For authors whose first language is not English, we recommend having their manuscripts reviewed and edited prior to submission by a native English speaker with scientific expertise. There are many commercial editing services which can provide this service at a cost to the authors.
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