Learning k-Inductive Control Barrier Certificates for Unknown Nonlinear Dynamics Beyond Polynomials
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| Published in: | arXiv.org (Dec 10, 2024), p. n/a |
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Cornell University Library, arXiv.org
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| Online Access: | Citation/Abstract Full text outside of ProQuest |
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| 001 | 3143055689 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 035 | |a 3143055689 | ||
| 045 | 0 | |b d20241210 | |
| 100 | 1 | |a Wooding, Ben | |
| 245 | 1 | |a Learning k-Inductive Control Barrier Certificates for Unknown Nonlinear Dynamics Beyond Polynomials | |
| 260 | |b Cornell University Library, arXiv.org |c Dec 10, 2024 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a This work is concerned with synthesizing safety controllers for discrete-time nonlinear systems beyond polynomials with unknown mathematical models using the notion of k-inductive control barrier certificates (k-CBCs). Conventional CBC conditions (with k=1) for ensuring safety over dynamical systems are often restrictive, as they require the CBCs to be non-increasing at every time step. Inspired by the success of k-induction in software verification, k-CBCs relax this requirement by allowing the barrier function to be non-increasing over k steps, while permitting k-1 (one-step) increases, each up to a threshold epsilon. This relaxation enhances the likelihood of finding feasible k-CBCs while providing safety guarantees across the dynamical systems. Despite showing promise, existing approaches for constructing k-CBCs often rely on precise mathematical knowledge of system dynamics, which is frequently unavailable in practical scenarios. In this work, we address the case where the underlying dynamics are unknown, a common occurrence in real-world applications, and employ the concept of persistency of excitation, grounded in Willems et al.'s fundamental lemma. This result implies that input-output data from a single trajectory can capture the behavior of an unknown system, provided the collected data fulfills a specific rank condition. We employ sum-of-squares (SOS) programming to synthesize the k-CBC as well as the safety controller directly from data while ensuring the safe behavior of the unknown system. The efficacy of our approach is demonstrated through a set of physical benchmarks with unknown dynamics, including a DC motor, an RLC circuit, a nonlinear nonpolynomial car, and a nonlinear polynomial Lorenz attractor. | |
| 653 | |a D C motors | ||
| 653 | |a Certificates | ||
| 653 | |a Polynomials | ||
| 653 | |a Electric motors | ||
| 653 | |a System dynamics | ||
| 653 | |a Program verification (computers) | ||
| 653 | |a Discrete time systems | ||
| 653 | |a Control systems | ||
| 653 | |a RLC circuits | ||
| 653 | |a Nonlinear systems | ||
| 653 | |a Dynamical systems | ||
| 653 | |a Nonlinear control | ||
| 653 | |a Synthesis | ||
| 653 | |a Nonlinear dynamics | ||
| 653 | |a Data collection | ||
| 700 | 1 | |a Lavaei, Abolfazl | |
| 773 | 0 | |t arXiv.org |g (Dec 10, 2024), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3143055689/abstract/embedded/ZKJTFFSVAI7CB62C?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/2412.07232 |