Formal synthesis of Lyapunov neural networks

A Abate, D Ahmed, M Giacobbe… - IEEE Control Systems …, 2020 - ieeexplore.ieee.org
We propose an automatic and formally sound method for synthesising Lyapunov functions
for the asymptotic stability of autonomous non-linear systems. Traditional methods are either …

FOSSIL: a software tool for the formal synthesis of lyapunov functions and barrier certificates using neural networks

A Abate, D Ahmed, A Edwards, M Giacobbe… - Proceedings of the 24th …, 2021 - dl.acm.org
This paper accompanies FOSSIL: a software tool for the synthesis of Lyapunov functions
and of barrier certificates (or functions) for dynamical systems modelled as differential …

Synthesizing ReLU neural networks with two hidden layers as barrier certificates for hybrid systems

Q Zhao, X Chen, Y Zhang, M Sha, Z Yang… - Proceedings of the 24th …, 2021 - dl.acm.org
Barrier certificates provide safety guarantees for hybrid systems. In this paper, we propose a
novel approach to synthesizing neural networks as barrier certificates. Candidate networks …

On completeness of SDP-based barrier certificate synthesis over unbounded domains

H Wu, S Feng, T Gan, J Wang, B **a, N Zhan - … Symposium on Formal …, 2024 - Springer
Barrier certificates, serving as differential invariants that witness system safety, play a crucial
role in the verification of cyber-physical systems (CPS). Prevailing computational methods …

[ΒΙΒΛΙΟ][B] Formal Verification of Simulink/Stateflow Diagrams

N Zhan, S Wang, H Zhao - 2017 - Springer
Our modern life increasingly depends on embedded systems. How to develop complex
embedded systems correctly is a grand challenge for computer science and control theory …

Formal techniques for verification and testing of cyber-physical systems

JV Deshmukh, S Sankaranarayanan - Design Automation of Cyber …, 2019 - Springer
Modern cyber-physical systems (CPS) are often developed in a model-based development
(MBD) paradigm. The MBD paradigm involves the construction of different kinds of …

Synthesizing invariant barrier certificates via difference-of-convex programming

Q Wang, M Chen, B Xue, N Zhan, JP Katoen - International Conference on …, 2021 - Springer
A barrier certificate often serves as an inductive invariant that isolates an unsafe region from
the reachable set of states, and hence is widely used in proving safety of hybrid systems …

A General Verification Framework for Dynamical and Control Models via Certificate Synthesis

A Edwards, A Peruffo, A Abate - arxiv preprint arxiv:2309.06090, 2023 - arxiv.org
An emerging branch of control theory specialises in certificate learning, concerning the
specification of a desired (possibly complex) system behaviour for an autonomous or control …

Linear relaxations of polynomial positivity for polynomial lyapunov function synthesis

MA Ben Sassi, S Sankaranarayanan… - IMA Journal of …, 2016 - academic.oup.com
We examine linear programming (LP) based relaxations for synthesizing polynomial
Lyapunov functions to prove the stability of polynomial ordinary differential equations …

Abstraction of elementary hybrid systems by variable transformation

J Liu, N Zhan, H Zhao, L Zou - International Symposium on Formal …, 2015 - Springer
Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing elementary
functions such as exp, ln, sin, cos, etc. EHSs are very common in practice, especially in …