Feedback control optimization of nonlinear systems under random excitations |
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| Institution: | 1. Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong;2. Peking University, Beijing 100871, China;3. AVIC Aerodynamics Research Institute, Harbin 150001, China;1. School of Materials Science and Engineering, Tianjin Key Lab for Photoelectric Materials & Devices, National Demonstration Center for Experimental Function Materials Education, Tianjin University of Technology, Tianjin 300384, China;2. Plant Protection Station, Zhangqiu Agriculture Bureau, Jinan, 250220, China;3. Tianjin Walkman Biomaterial Co., Ltd., Tianjin 300384, China;4. Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, China;1. Research Institute of Automotive Engineering, Jiangsu University, Zhenjiang 212013, People’s Republic of China;2. School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, People’s Republic of China |
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| Abstract: | This paper uses stochastic averaging method to design an optimal feedback control for nonlinear stochastic systems. The method of stochastic averaging is used to reduce the dimension of the state space and to derive the Itô stochastic differential equation for the response amplitude process. Two approaches to optimization, namely, with the exact steady state probability density function of the amplitude process and the Rayleigh approximation are compared. The cost function is a steady state response measure. Numerical examples are studied to demonstrate the performance of the control both in transient and steady-state. The effect of the control on the system response and control performance is studied. The regions where the controls are conservative and unconservative are pointed out. |
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