From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems

Behrad Samari; Omid Akbarzadeh; Mahdieh Zaker; Abolfazl Lavaei

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arXiv · 2409.10026

From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems

Behrad Samari·Omid Akbarzadeh·Mahdieh Zaker·Abolfazl Lavaei

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Abstract

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.

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BibTeX RIS

Behrad Samari, Omid Akbarzadeh, Mahdieh Zaker, Abolfazl Lavaei. 2024-09-16. From a Single Trajectory to Safety Controller Synthesis of Discrete-Time Nonlinear Polynomial Systems. https://arxiv.org/abs/2409.10026

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