Stochastic Optimal Control for Uncertain Structural Systems Under Random Excitations Based on Bayes Optimal Estimation
Stochastic vibration control of uncertain structures under random loading is an important problem and its minimax optimal control strategy remains to be developed. In this paper, a stochastic optimal control strategy for uncertain structural systems under random excitations is proposed, based on the...
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2025-05-01
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| author | Hua Lei Zhao-Zhong Ying Zu-Guang Ying |
| author_facet | Hua Lei Zhao-Zhong Ying Zu-Guang Ying |
| author_sort | Hua Lei |
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| description | Stochastic vibration control of uncertain structures under random loading is an important problem and its minimax optimal control strategy remains to be developed. In this paper, a stochastic optimal control strategy for uncertain structural systems under random excitations is proposed, based on the minimax stochastic dynamical programming principle and the Bayes optimal estimation method with the combination of stochastic dynamics and Bayes inference. The general description of the stochastic optimal control problem is presented including optimal parameter estimation and optimal state control. For the estimation, the posterior probability density conditional on observation states is expressed using the likelihood function conditional on system parameters according to Bayes’ theorem. The likelihood is replaced by the geometrically averaged likelihood, and the posterior is converted into its logarithmic expression to avoid numerical singularity. The expressions of state statistics are derived based on stochastic dynamics. The statistics are further transformed into those conditional on observation states based on optimal state estimation. Then, the obtained posterior will be more reliable and accurate, and the optimal estimation will greatly reduce uncertain parameter domains. For the control, the minimax strategy is designed by minimizing the performance index for the worst-parameter system, which is obtained by maximizing the performance index based on game theory. The dynamical programming equation for the uncertain system is derived according to the minimax stochastic dynamical programming principle. The worst parameters are determined by the maximization of the equation, and the optimal control is determined by the minimization of the resulting equation. The minimax optimal control by combining the Bayes optimal estimation and minimax stochastic dynamical programming will be more effective and robust. Finally, numerical results for a five-story frame structure under random excitations show the control effectiveness of the proposed strategy. |
| format | Article |
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| language | English |
| publishDate | 2025-05-01 |
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| spelling | doaj-art-c0bf705ec2d8443db175d9d041848aba2025-08-20T02:24:47ZengMDPI AGBuildings2075-53092025-05-01159157910.3390/buildings15091579Stochastic Optimal Control for Uncertain Structural Systems Under Random Excitations Based on Bayes Optimal EstimationHua Lei0Zhao-Zhong Ying1Zu-Guang Ying2Department of Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, ChinaHoongjun Micro Electronic Technology Company, Hangzhou 311202, ChinaDepartment of Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, ChinaStochastic vibration control of uncertain structures under random loading is an important problem and its minimax optimal control strategy remains to be developed. In this paper, a stochastic optimal control strategy for uncertain structural systems under random excitations is proposed, based on the minimax stochastic dynamical programming principle and the Bayes optimal estimation method with the combination of stochastic dynamics and Bayes inference. The general description of the stochastic optimal control problem is presented including optimal parameter estimation and optimal state control. For the estimation, the posterior probability density conditional on observation states is expressed using the likelihood function conditional on system parameters according to Bayes’ theorem. The likelihood is replaced by the geometrically averaged likelihood, and the posterior is converted into its logarithmic expression to avoid numerical singularity. The expressions of state statistics are derived based on stochastic dynamics. The statistics are further transformed into those conditional on observation states based on optimal state estimation. Then, the obtained posterior will be more reliable and accurate, and the optimal estimation will greatly reduce uncertain parameter domains. For the control, the minimax strategy is designed by minimizing the performance index for the worst-parameter system, which is obtained by maximizing the performance index based on game theory. The dynamical programming equation for the uncertain system is derived according to the minimax stochastic dynamical programming principle. The worst parameters are determined by the maximization of the equation, and the optimal control is determined by the minimization of the resulting equation. The minimax optimal control by combining the Bayes optimal estimation and minimax stochastic dynamical programming will be more effective and robust. Finally, numerical results for a five-story frame structure under random excitations show the control effectiveness of the proposed strategy.https://www.mdpi.com/2075-5309/15/9/1579stochastic optimal controloptimal parameter estimationBayes inferencestochastic dynamical programminguncertain structure systemminimax strategy |
| spellingShingle | Hua Lei Zhao-Zhong Ying Zu-Guang Ying Stochastic Optimal Control for Uncertain Structural Systems Under Random Excitations Based on Bayes Optimal Estimation Buildings stochastic optimal control optimal parameter estimation Bayes inference stochastic dynamical programming uncertain structure system minimax strategy |
| title | Stochastic Optimal Control for Uncertain Structural Systems Under Random Excitations Based on Bayes Optimal Estimation |
| title_full | Stochastic Optimal Control for Uncertain Structural Systems Under Random Excitations Based on Bayes Optimal Estimation |
| title_fullStr | Stochastic Optimal Control for Uncertain Structural Systems Under Random Excitations Based on Bayes Optimal Estimation |
| title_full_unstemmed | Stochastic Optimal Control for Uncertain Structural Systems Under Random Excitations Based on Bayes Optimal Estimation |
| title_short | Stochastic Optimal Control for Uncertain Structural Systems Under Random Excitations Based on Bayes Optimal Estimation |
| title_sort | stochastic optimal control for uncertain structural systems under random excitations based on bayes optimal estimation |
| topic | stochastic optimal control optimal parameter estimation Bayes inference stochastic dynamical programming uncertain structure system minimax strategy |
| url | https://www.mdpi.com/2075-5309/15/9/1579 |
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