Backstepping Synthesis for Feedback Control of First‐Order Hyperbolic PDEs with Spatial‐Temporal Actuation

Xin Yu, Chao Xu, Huacheng Jiang, Arthi Ganesan and Guojie Zheng

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: This paper deals with the stabilization problem of first‐order hyperbolic partial differential equations (PDEs) with spatial‐temporal actuation over the full physical domains. We assume that the interior actuator can be decomposed into a product of spatial and temporal components, where the spatial component satisfies a specific ordinary differential equation (ODE). A Volterra integral transformation is used to convert the original system into a simple target system using the backstepping‐like procedure. Unlike the classical backstepping techniques for boundary control problems of PDEs, the internal actuation can not eliminate the residual term that causes the instability of the open‐loop system. Thus, an additional differential transformation is introduced to transfer the input from the interior of the domain onto the boundary. Then, a feedback control law is designed using the classic backstepping technique which can stabilize the first‐order hyperbolic PDE system in a finite time, which can be proved by using the semigroup arguments. The effectiveness of the design is illustrated with some numerical simulations.

Date: 2014
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https://doi.org/10.1155/2014/643640

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:643640

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