Synthesis of safety certificates for discrete-time uncertain systems via convex optimization
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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_ | 1866915286409543680 |
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| author | Fochesato, Marta Wang, Han Papachristodoulou, Antonis Goulart, Paul |
| author_facet | Fochesato, Marta Wang, Han Papachristodoulou, Antonis Goulart, Paul |
| contents | We study the problem of co-designing control barrier functions and linear state feedback controllers for discrete-time linear systems affected by additive disturbances. For disturbances of bounded magnitude, we provide a semi-definite program whose feasibility implies the existence of a control law and a certificate ensuring safety in the infinite horizon with respect to the worst-case disturbance realization in the uncertainty set. For disturbances with unbounded support, we rely on martingale theory to derive a second semi-definite program whose feasibility provides probabilistic safety guarantees holding joint-in-time over a finite time horizon. We examine several extensions, including (i) encoding of different types of input constraints, (ii) robustification against distributional ambiguity around the true distribution, (iii) design of safety filters, and (iv) extension to general safety specifications such as obstacle avoidance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Synthesis of safety certificates for discrete-time uncertain systems via convex optimization Fochesato, Marta Wang, Han Papachristodoulou, Antonis Goulart, Paul Optimization and Control Systems and Control We study the problem of co-designing control barrier functions and linear state feedback controllers for discrete-time linear systems affected by additive disturbances. For disturbances of bounded magnitude, we provide a semi-definite program whose feasibility implies the existence of a control law and a certificate ensuring safety in the infinite horizon with respect to the worst-case disturbance realization in the uncertainty set. For disturbances with unbounded support, we rely on martingale theory to derive a second semi-definite program whose feasibility provides probabilistic safety guarantees holding joint-in-time over a finite time horizon. We examine several extensions, including (i) encoding of different types of input constraints, (ii) robustification against distributional ambiguity around the true distribution, (iii) design of safety filters, and (iv) extension to general safety specifications such as obstacle avoidance. |
| title | Synthesis of safety certificates for discrete-time uncertain systems via convex optimization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2505.08559 |