Sparse $H_\infty$ Controller for Networked Control Systems: Non-Structured and Optimal Structured Design
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910928654565376 |
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| author | Yang, Zhaohua Wang, Pengyu Zhang, Haishan Jia, Shiyue Yang, Nachuan Zhong, Yuxing Shi, Ling |
| author_facet | Yang, Zhaohua Wang, Pengyu Zhang, Haishan Jia, Shiyue Yang, Nachuan Zhong, Yuxing Shi, Ling |
| contents | This paper provides a comprehensive analysis of the design of optimal structured and sparse $H_\infty$ controllers for continuous-time linear time-invariant (LTI) systems. Three problems are considered. First, designing the sparsest $H_\infty$ controller, which minimizes the sparsity of the controller while satisfying the given performance requirements. Second, designing a sparsity-promoting $H_\infty$ controller, which balances system performance and controller sparsity. Third, designing a $H_\infty$ controller subject to a structural constraint, which enhances system performance with a specified sparsity pattern. For each problem, we adopt a linearization technique that transforms the original nonconvex problem into a convex semidefinite programming (SDP) problem. Subsequently, we design an iterative linear matrix inequality (ILMI) algorithm for each problem, which ensures guaranteed convergence. We further characterize the first-order optimality using the Karush-Kuhn-Tucker (KKT) conditions and prove that any limit point of the solution sequence generated by the ILMI algorithm is a stationary point. For the first and second problems, we validate that our algorithms can reduce the number of non-zero elements and thus the communication burden through several numerical simulations. For the third problem, we refine the solutions obtained in existing literature, demonstrating that our approaches achieve significant improvements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse $H_\infty$ Controller for Networked Control Systems: Non-Structured and Optimal Structured Design Yang, Zhaohua Wang, Pengyu Zhang, Haishan Jia, Shiyue Yang, Nachuan Zhong, Yuxing Shi, Ling Optimization and Control This paper provides a comprehensive analysis of the design of optimal structured and sparse $H_\infty$ controllers for continuous-time linear time-invariant (LTI) systems. Three problems are considered. First, designing the sparsest $H_\infty$ controller, which minimizes the sparsity of the controller while satisfying the given performance requirements. Second, designing a sparsity-promoting $H_\infty$ controller, which balances system performance and controller sparsity. Third, designing a $H_\infty$ controller subject to a structural constraint, which enhances system performance with a specified sparsity pattern. For each problem, we adopt a linearization technique that transforms the original nonconvex problem into a convex semidefinite programming (SDP) problem. Subsequently, we design an iterative linear matrix inequality (ILMI) algorithm for each problem, which ensures guaranteed convergence. We further characterize the first-order optimality using the Karush-Kuhn-Tucker (KKT) conditions and prove that any limit point of the solution sequence generated by the ILMI algorithm is a stationary point. For the first and second problems, we validate that our algorithms can reduce the number of non-zero elements and thus the communication burden through several numerical simulations. For the third problem, we refine the solutions obtained in existing literature, demonstrating that our approaches achieve significant improvements. |
| title | Sparse $H_\infty$ Controller for Networked Control Systems: Non-Structured and Optimal Structured Design |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2411.00370 |