{"title":"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","authors":"Z. Ying, R. Hu, R. Huan","doi":"10.20855/ijav.2019.24.41446","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":49185,"journal":{"name":"International Journal of Acoustics and Vibration","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stochastic Minimax Vibration Control for Uncertain Nonlinear Quasi-Hamiltonian Systems with Noisy Observations\",\"authors\":\"Z. Ying, R. Hu, R. Huan\",\"doi\":\"10.20855/ijav.2019.24.41446\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":49185,\"journal\":{\"name\":\"International Journal of Acoustics and Vibration\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2019-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Acoustics and Vibration\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.20855/ijav.2019.24.41446\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Acoustics and Vibration","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.20855/ijav.2019.24.41446","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ACOUSTICS","Score":null,"Total":0}
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.
期刊介绍:
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