Certifying the Intersection of Reach Sets of Integrator Agents with Set-valued Input Uncertainties
Optimization and Control
2022-05-19 v4 Systems and Control
Systems and Control
Abstract
We consider the problem of verifying safety for a pair of identical integrator agents in continuous time with compact set-valued input uncertainties. We encode this verification problem as that of certifying or falsifying the intersection of their reach sets. We transcribe the same into a variational problem, namely that of minimizing the support function of the difference of the two reach sets over the unit sphere. We illustrate the computational tractability of the proposed formulation by developing two cases in detail, viz. when the inputs have time-varying norm-bounded and generic hyperrectangular uncertainties. We show that the latter case allows distributed certification via second order cone programming.
Keywords
Cite
@article{arxiv.2203.12007,
title = {Certifying the Intersection of Reach Sets of Integrator Agents with Set-valued Input Uncertainties},
author = {Shadi Haddad and Abhishek Halder},
journal= {arXiv preprint arXiv:2203.12007},
year = {2022}
}