Towards a Framework for Realizable Safety Critical Control through Active Set Invariance

Abstract

This paper presents initial results towards a realizable framework for the safety critical controlled invariance of cyber-physical systems. The main contribution of this paper is the development of a control barrier function based methodology which can be used to enforce set invariance on systems in the presence of non-linear disturbances and uncertainty. The first part of this work is a review of the current methods available for finding viable sets and how they are linked to practical choices regarding safety. Their limitations and directions towards improvements when it comes to handling model uncertainty are also highlighted. The second part of this work is the formulation of a condition which can guarantee set invariance in the presence of generic uncertain in the dynamics. An associated optimization problem to enforce that condition is proposed and a method to convexify the problem and make it solvable in real-time is formally presented. The effectiveness of the proposed framework is illustrated experimentally on a two-wheeled inverted pendulum.