Backstepping Boundary Control for Unstable Second-Order Hyperbolic PDEs and Trajectory Tracking
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In this paper, a problem of boundary feedback stabilization of second order hyperbolic partial differential equations (PDEs) is considered. These equations serve as a model for physical phenomena such as oscillatory systems like strings and beams. The controllers are designed using a backstepping method, which has been recently developed for parabolic PDEs. With the integral transformation and boundary feedback the unstable PDE is converted into a system which is stable in sense of Lyapunov. Then taylorian expansion is used to achieve the goal of trajectory tracking. It means design a boundary controller such that output of the system follows an arbitrary map. The designs are illustrated with simulations.
2011 ◽
Vol 219-220
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pp. 957-960
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2004 ◽
Vol 21
(1)
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pp. 169-184
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2012 ◽
Vol 388
(2)
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pp. 676-694
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2013 ◽
Vol 46
(13)
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pp. 100-104
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