Boundary stabilization of a class of reaction–advection–diffusion systems via a gradient-based optimization approach |
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| Authors: | Zhigang Ren Chao Xu Zhongcheng Zhou Zongze Wu Tehuan Chen |
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| Institution: | 1. School of Automation and Guangdong Key Laboratory of IoT Information Technology, Guangdong University of Technology, Guangzhou, Guangdong, China;2. State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control, Zhejiang University, Hangzhou, Zhejiang, China;3. School of Mathematics & Statistics, Southwest University, Chongqing, China;4. Faculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo, Zhejiang, China |
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| Abstract: | In this paper, the boundary stabilization problem of a class of unstable reaction–advection–diffusion (RAD) systems described by a scalar parabolic partial differential equation (PDE) is considered. Different the previous research, we present a new gradient-based optimization framework for designing the optimal feedback kernel for stabilizing the unstable PDE system. Our new method does not require solving non-standard Riccati-type or Klein–Gorden-type PDEs. Instead, the feedback kernel is parameterized as a second-order polynomial whose coefficients are decision variables to be tuned via gradient-based dynamic optimization, where the gradients of the system cost functional (which penalizes both kernel and output magnitude) with respect to the decision parameters are computed by solving a so-called “costate” PDE in standard form. Special constraints are imposed on the kernel coefficients to ensure that the optimized kernel yields closed-loop stability. Finally, three numerical examples are illustrated to verify the effectiveness of the proposed approach. |
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| Keywords: | Corresponding author |
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