Lyapunov-based design of locally collocated controllers for semi-linear parabolic PDE systems |
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| Authors: | Jun-Wei Wang Huai-Ning Wu |
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| Institution: | 1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University (Beijing University of Aeronautics and Astronautics), Beijing 100191, China |
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| Abstract: | The design problem of collocated feedback controllers is addressed in this paper for a class of semi-linear distributed parameter systems described by parabolic partial differential equation (PDE), where a finite number of local actuators and sensors are intermittently distributed in space. A Lyapunov direct method for the exponential stability analysis of the resulting closed-loop system is first presented for the system, in which the first mean value theorem for integration and the Wirtinger's inequality are employed. The corresponding stabilization condition is then derived through the analysis result. Finally, the proposed design method is implemented on the feedback control of a fisher equation and its effectiveness is evaluated through simulation results. |
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| Keywords: | Distributed parameter systems Exponential stability Collocated actuators and sensors Mean value theorem Fisher equation |
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