From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems
<|reference_start|>From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems: 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.<|reference_end|>
@article{samari2024from,
    title={From a Single Trajectory to Safety Controller Synthesis of Discrete-Time
  Nonlinear Polynomial Systems},
    author={Behrad Samari, Omid Akbarzadeh, Mahdieh Zaker, Abolfazl Lavaei},
    journal={arXiv preprint arXiv:2409.10026},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.10026},
    primaryClass={eess.SY cs.SY}
}