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Title
Japanese: 
English:Inverse Optimal Control Problem for Bilinear Systems: Application to the Inverted Pendulum with Horizontal and Vertical Movement 
Author
Japanese: 金澤 雅夫, 中浦 茂樹, 三平 満司.  
English: Masao Kanazawa, Shigeki Nakaura, Mitsuji Sampei.  
Language English 
Journal/Book name
Japanese: 
English:Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference 
Volume, Number, Page         pp. 2260-2267
Published date Dec. 2009 
Publisher
Japanese: 
English:IEEE 
Conference name
Japanese: 
English:48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference 
Conference site
Japanese:中国、上海 
English:Shanghai, China 
DOI https://doi.org/10.1109/CDC.2009.5399912
Abstract Inverse optimal design for bilinear systems is considered. The main result is that a nonlinear optimal feedback control law which minimizes a new quadratic cost function with nonlinear weight is obtained based on an inverse optimal control problem for bilinear systems. This inverse optimal control design is applied to the problem of the stabilization of the inverted pendulum on the cart which moves not only in the horizontal direction but also in the vertical direction. This inverted pendulum system can be transformed into a bilinear system by using input transformation and coordinate transformation forcused on the center of percussion of the pendulum. It is theoretically shown that the proposed nonlinear optimal feedback controller has higher control performance than a conventional linear optimal controller for the linear approximation system. Furthermore, it is shown by numerical simulations that the control performance of the pendulum is improved by utilizing the vertical movement of the pendulum.

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