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Boundary Control of Coupled Wave Systems with spatially-varying coefficients

Journal of Systems Science & Complexity 2022年第4期35卷 1310-1329页

作者： FENG Xiaodan ZHANG Zhifei School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074China

This paper considers the stabilization of the coupled wave systems with spatially-varying *** authors design a state feedback controller by backstepping *** contrast to the previous work in the literature,the kernel equations become more complicated and the main difficulty lies in proving the existence and uniqueness of the solution to the kernel ***,using the backstepping approach,the authors verify the kernel equations,which is a system of coupled hyperbolic equations with spatially-varying ***,the existence and uniqueness of the kernel matrices is ***,the authors use a Lyapunov function to get the exponential stabilization of the closed-loop system.A numerical example is presented to illustrate the effectiveness of the proposed controller.

关键词： Backstepping boundary control coupled wave systems exponential stabilization spatially-varying coefficients

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Boundary stabilization of coupled wave system with spatially-varying coefficients and internal anti-damping

Boundary stabilization of coupled wave system with spatially...

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第三十九届中国控制会议

作者： Xiaodan Feng Zhifei Zhang Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology

In this paper, we consider the exponential stabilization of coupled wave equations with spatially-varying coefficients and internal anti-damping. In contrast to the previous work in the literature, the kernel equations of this system are much more complicated. Using the backstepping method, we verify the kernel equations, which is a system of coupled linear wave equations with spatially-varying coefficients. Then by designing a new characteristic line, the well-posedness of the kernel equations is obtained. Finally we use a Lyapunov function to get the exponential stabilization. A numerical example is presented to illustrate the result.

关键词： backstepping boundary control coupled wave system spatially-varying coefficients

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