From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913501518233600 |
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| author | Samari, Behrad Akbarzadeh, Omid Zaker, Mahdieh Lavaei, Abolfazl |
| author_facet | Samari, Behrad Akbarzadeh, Omid Zaker, Mahdieh Lavaei, Abolfazl |
| contents | This work is concerned with developing a data-driven approach for learning control barrier certificates (CBCs) and associated safety controllers for discrete-time nonlinear polynomial systems with unknown mathematical models, guaranteeing system safety over an infinite time horizon. The proposed approach leverages measured data acquired through an input-output observation, referred to as a single trajectory, collected over a specified time horizon. By fulfilling a certain rank condition, which ensures the unknown system is persistently excited by the collected data, we design a CBC and its corresponding safety controller directly from the finite-length observed data, without explicitly identifying the unknown dynamical system. This is achieved through proposing a data-based sum-of-squares optimization (SOS) program to systematically design CBCs and their safety controllers. We validate our data-driven approach over two physical case studies including a jet engine and a Lorenz system, demonstrating the efficacy of our proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10026 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems Samari, Behrad Akbarzadeh, Omid Zaker, Mahdieh Lavaei, Abolfazl Systems and Control This work is concerned with developing a data-driven approach for learning control barrier certificates (CBCs) and associated safety controllers for discrete-time nonlinear polynomial systems with unknown mathematical models, guaranteeing system safety over an infinite time horizon. The proposed approach leverages measured data acquired through an input-output observation, referred to as a single trajectory, collected over a specified time horizon. By fulfilling a certain rank condition, which ensures the unknown system is persistently excited by the collected data, we design a CBC and its corresponding safety controller directly from the finite-length observed data, without explicitly identifying the unknown dynamical system. This is achieved through proposing a data-based sum-of-squares optimization (SOS) program to systematically design CBCs and their safety controllers. We validate our data-driven approach over two physical case studies including a jet engine and a Lorenz system, demonstrating the efficacy of our proposed method. |
| title | From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2409.10026 |