A new computational method for sparse optimal control of cyber-physical systems with varying delay
In practice, network operators tend to choose sparse communication topologies to cut costs, and the concurrent use of a communication network by multiple users commonly results in feedback delays. Our goal was to obtain the optimal sparse feedback control matrix $ K $. For this, we proposed a sparse...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024306 |
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| _version_ | 1832590783448875008 |
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| author | Sida Lin Dongyao Yang Jinlong Yuan Changzhi Wu Tao Zhou An Li Chuanye Gu Jun Xie Kuikui Gao |
| author_facet | Sida Lin Dongyao Yang Jinlong Yuan Changzhi Wu Tao Zhou An Li Chuanye Gu Jun Xie Kuikui Gao |
| author_sort | Sida Lin |
| collection | DOAJ |
| description | In practice, network operators tend to choose sparse communication topologies to cut costs, and the concurrent use of a communication network by multiple users commonly results in feedback delays. Our goal was to obtain the optimal sparse feedback control matrix $ K $. For this, we proposed a sparse optimal control (SOC) problem governed by the cyber-physical system with varying delay, to minimize $ ||K||_0 $ subject to a maximum allowable compromise in system cost. A penalty method was utilized to transform the SOC problem into a form that was constrained solely by box constraints. A smoothing technique was used to approximate the nonsmooth element in the resulting problem, and an analysis of the errors introduced by this technique was subsequently conducted. The gradients of the objective function concerning the feedback control matrix were obtained by solving the state system and a variational system simultaneously forward in time. An optimization algorithm was devised to tackle the resulting problem, building on the piecewise quadratic approximation. Finally, we have presented of simulations. |
| format | Article |
| id | doaj-art-e8999c791c9b433cb0f323e61d62b981 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-e8999c791c9b433cb0f323e61d62b9812025-01-23T07:53:06ZengAIMS PressElectronic Research Archive2688-15942024-12-0132126553657710.3934/era.2024306A new computational method for sparse optimal control of cyber-physical systems with varying delaySida Lin0Dongyao Yang1Jinlong Yuan2Changzhi Wu3Tao Zhou4An Li5Chuanye Gu6Jun Xie7Kuikui Gao8School of Science, Dalian Maritime University, Dalian 116026, ChinaSchool of Science, Dalian Maritime University, Dalian 116026, ChinaSchool of Science, Dalian Maritime University, Dalian 116026, ChinaChongqing National Center for Applied Mathematics, Chongqing Normal University, Chongqing 404087, ChinaInstitute for Intelligent Systems Research and Innovation (IISRI), Deakin University, Geelong 3217, AustraliaSchool of Mathematical Sciences, Xiamen University, Xiamen 361005, ChinaSchool of Management, Guangzhou University, Guangzhou 510006, ChinaDepartment of Basics, PLA Dalian Naval Academy, Dalian 116018, ChinaAyata Incorporation, 2700 Post Oak Blvd, 21st Floor, Houston, TX 77056, USAIn practice, network operators tend to choose sparse communication topologies to cut costs, and the concurrent use of a communication network by multiple users commonly results in feedback delays. Our goal was to obtain the optimal sparse feedback control matrix $ K $. For this, we proposed a sparse optimal control (SOC) problem governed by the cyber-physical system with varying delay, to minimize $ ||K||_0 $ subject to a maximum allowable compromise in system cost. A penalty method was utilized to transform the SOC problem into a form that was constrained solely by box constraints. A smoothing technique was used to approximate the nonsmooth element in the resulting problem, and an analysis of the errors introduced by this technique was subsequently conducted. The gradients of the objective function concerning the feedback control matrix were obtained by solving the state system and a variational system simultaneously forward in time. An optimization algorithm was devised to tackle the resulting problem, building on the piecewise quadratic approximation. Finally, we have presented of simulations.https://www.aimspress.com/article/doi/10.3934/era.2024306cyber-physical system$ l_0 $-norm of a matrixsparse feedback matrixvarying delaysmoothing technique |
| spellingShingle | Sida Lin Dongyao Yang Jinlong Yuan Changzhi Wu Tao Zhou An Li Chuanye Gu Jun Xie Kuikui Gao A new computational method for sparse optimal control of cyber-physical systems with varying delay Electronic Research Archive cyber-physical system $ l_0 $-norm of a matrix sparse feedback matrix varying delay smoothing technique |
| title | A new computational method for sparse optimal control of cyber-physical systems with varying delay |
| title_full | A new computational method for sparse optimal control of cyber-physical systems with varying delay |
| title_fullStr | A new computational method for sparse optimal control of cyber-physical systems with varying delay |
| title_full_unstemmed | A new computational method for sparse optimal control of cyber-physical systems with varying delay |
| title_short | A new computational method for sparse optimal control of cyber-physical systems with varying delay |
| title_sort | new computational method for sparse optimal control of cyber physical systems with varying delay |
| topic | cyber-physical system $ l_0 $-norm of a matrix sparse feedback matrix varying delay smoothing technique |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024306 |
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