Sparse optimal control for infinite-dimensional linear systems with applications to graphon control
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908463974580224 |
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| author | Ikeda, Takuya Nagahara, Masaaki |
| author_facet | Ikeda, Takuya Nagahara, Masaaki |
| contents | Large-scale networked systems typically operate under resource constraints, and it is also difficult to exactly obtain the network structure between nodes. To address these issues, this paper investigates a sparse optimal control for infinite-dimensional linear systems and its application to networked systems where the network structure is represented by a limit function called a graphon that captures the overall connection pattern. The contributions of this paper are twofold: (i) To reduce computational complexity, we derive a sufficient condition under which the sparse optimal control can be obtained by solving its corresponding L1 optimization problem. Furthermore, we introduce a class of non-convex optimal control problems such that the optimal solution always coincides with a sparse optimal control, provided that the non-convex problems admit optimal solutions. (ii) We show that the sparse optimal control for large-scale finite-dimensional networked systems can be approximated by that of the corresponding limit graphon system, provided that the underlying graph is close to the limit graphon in the cut-norm topology. The effectiveness of the proposed approach is illustrated through numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18030 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sparse optimal control for infinite-dimensional linear systems with applications to graphon control Ikeda, Takuya Nagahara, Masaaki Optimization and Control Systems and Control Large-scale networked systems typically operate under resource constraints, and it is also difficult to exactly obtain the network structure between nodes. To address these issues, this paper investigates a sparse optimal control for infinite-dimensional linear systems and its application to networked systems where the network structure is represented by a limit function called a graphon that captures the overall connection pattern. The contributions of this paper are twofold: (i) To reduce computational complexity, we derive a sufficient condition under which the sparse optimal control can be obtained by solving its corresponding L1 optimization problem. Furthermore, we introduce a class of non-convex optimal control problems such that the optimal solution always coincides with a sparse optimal control, provided that the non-convex problems admit optimal solutions. (ii) We show that the sparse optimal control for large-scale finite-dimensional networked systems can be approximated by that of the corresponding limit graphon system, provided that the underlying graph is close to the limit graphon in the cut-norm topology. The effectiveness of the proposed approach is illustrated through numerical examples. |
| title | Sparse optimal control for infinite-dimensional linear systems with applications to graphon control |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2507.18030 |