Synthesis of Discrete-time Control Barrier Functions for Polynomial Systems Based on Sum-of-Squares Programming
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918003592921088 |
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| author | Shakhesi, Erfan Heemels, W. P. M. H. Katriniok, Alexander |
| author_facet | Shakhesi, Erfan Heemels, W. P. M. H. Katriniok, Alexander |
| contents | Discrete-time Control Barrier Functions (DTCBFs) are commonly utilized in the literature as a powerful tool for synthesizing control policies that guarantee safety of discrete-time dynamical systems. However, the systematic synthesis of DTCBFs in a computationally efficient way is at present an important open problem. This article first proposes a novel alternating-descent approach based on Sum-of-Squares programming to synthesize quadratic DTCBFs and corresponding polynomial control policies for discrete-time control-affine polynomial systems with input constraints and semi-algebraic safe sets. Subsequently, two distinct approaches are introduced to extend the proposed method to the synthesis of higher-degree polynomial DTCBFs. To demonstrate its efficacy, we apply the proposed method to numerical case studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Synthesis of Discrete-time Control Barrier Functions for Polynomial Systems Based on Sum-of-Squares Programming Shakhesi, Erfan Heemels, W. P. M. H. Katriniok, Alexander Optimization and Control Systems and Control Discrete-time Control Barrier Functions (DTCBFs) are commonly utilized in the literature as a powerful tool for synthesizing control policies that guarantee safety of discrete-time dynamical systems. However, the systematic synthesis of DTCBFs in a computationally efficient way is at present an important open problem. This article first proposes a novel alternating-descent approach based on Sum-of-Squares programming to synthesize quadratic DTCBFs and corresponding polynomial control policies for discrete-time control-affine polynomial systems with input constraints and semi-algebraic safe sets. Subsequently, two distinct approaches are introduced to extend the proposed method to the synthesis of higher-degree polynomial DTCBFs. To demonstrate its efficacy, we apply the proposed method to numerical case studies. |
| title | Synthesis of Discrete-time Control Barrier Functions for Polynomial Systems Based on Sum-of-Squares Programming |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2504.19330 |