A Gradient-based Kernel Optimization Approach for Parabolic Distributed Parameter Control Systems

This paper proposes a new gradient-based optimization approach for designing optimal feedback kernels for parabolic distributed parameter systems with boundary control. Unlike traditional kernel optimization methods for parabolic systems, our new method does not require solving non-standard Riccati-...

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Main Authors: Ren, Z., Xu, C., Lin, Qun, Loxton, Ryan
Format: Journal Article
Published: Yokohama Publishers 2016
Online Access:http://www.ybook.co.jp/online2/oppjo/vol12/p263.html
http://hdl.handle.net/20.500.11937/21022
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author Ren, Z.
Xu, C.
Lin, Qun
Loxton, Ryan
author_facet Ren, Z.
Xu, C.
Lin, Qun
Loxton, Ryan
author_sort Ren, Z.
building Curtin Institutional Repository
collection Online Access
description This paper proposes a new gradient-based optimization approach for designing optimal feedback kernels for parabolic distributed parameter systems with boundary control. Unlike traditional kernel optimization methods for parabolic systems, our new method does not require solving non-standard Riccati-type or Klein-Gorden-type partial differential equations (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 gradient of the system cost functional (which penalizes both kernel and output magnitude) is computed by solving a so-called “costate" PDE in standard form. Special constraints are imposed on the kernel coefficients to ensure that, under mild conditions, the optimized kernel yields closed-loop stability. Numerical simulations demonstrate the effectiveness of the proposed approach.
first_indexed 2025-11-14T07:37:24Z
format Journal Article
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institution Curtin University Malaysia
institution_category Local University
last_indexed 2025-11-14T07:37:24Z
publishDate 2016
publisher Yokohama Publishers
recordtype eprints
repository_type Digital Repository
spelling curtin-20.500.11937-210222018-03-26T09:09:56Z A Gradient-based Kernel Optimization Approach for Parabolic Distributed Parameter Control Systems Ren, Z. Xu, C. Lin, Qun Loxton, Ryan This paper proposes a new gradient-based optimization approach for designing optimal feedback kernels for parabolic distributed parameter systems with boundary control. Unlike traditional kernel optimization methods for parabolic systems, our new method does not require solving non-standard Riccati-type or Klein-Gorden-type partial differential equations (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 gradient of the system cost functional (which penalizes both kernel and output magnitude) is computed by solving a so-called “costate" PDE in standard form. Special constraints are imposed on the kernel coefficients to ensure that, under mild conditions, the optimized kernel yields closed-loop stability. Numerical simulations demonstrate the effectiveness of the proposed approach. 2016 Journal Article http://hdl.handle.net/20.500.11937/21022 http://www.ybook.co.jp/online2/oppjo/vol12/p263.html Yokohama Publishers unknown
spellingShingle Ren, Z.
Xu, C.
Lin, Qun
Loxton, Ryan
A Gradient-based Kernel Optimization Approach for Parabolic Distributed Parameter Control Systems
title A Gradient-based Kernel Optimization Approach for Parabolic Distributed Parameter Control Systems
title_full A Gradient-based Kernel Optimization Approach for Parabolic Distributed Parameter Control Systems
title_fullStr A Gradient-based Kernel Optimization Approach for Parabolic Distributed Parameter Control Systems
title_full_unstemmed A Gradient-based Kernel Optimization Approach for Parabolic Distributed Parameter Control Systems
title_short A Gradient-based Kernel Optimization Approach for Parabolic Distributed Parameter Control Systems
title_sort gradient-based kernel optimization approach for parabolic distributed parameter control systems
url http://www.ybook.co.jp/online2/oppjo/vol12/p263.html
http://hdl.handle.net/20.500.11937/21022