Safety Verification for Distributed Parameter Systems Using Barrier Functionals
Abstract
We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of constraints at a particular point in time. The proposed method is based on an extension of barrier certificates to infinite-dimensional systems. In this respect, we introduce barrier functionals, which are functionals of the dependent and independent variables. Given a set of initial conditions and an unsafe set, we demonstrate that if such a functional exists satisfying two (integral) inequalities, then the solutions of the system do not enter the unsafe set. Therefore, the proposed method does not require finite-dimensional approximations of the distributed parameter system. Furthermore, for PDEs with polynomial data, we solve the associated integral inequalities using semi-definite programming (SDP) based on a method that relies on a quadratic representation of the integrands of integral inequalities. The proposed method is illustrated through examples.
Cite
@article{arxiv.1708.03219,
title = {Safety Verification for Distributed Parameter Systems Using Barrier Functionals},
author = {Mohamadreza Ahmadi and Giorgio Valmorbida and Antonis Papachristodoulou},
journal= {arXiv preprint arXiv:1708.03219},
year = {2017}
}
Comments
Preprint under review at Systems and Control Letters. arXiv admin note: text overlap with arXiv:1603.08716