Certifying Safety for Nonlinear Time Delay Systems via Safety Functionals: A Discretization Based Approach

In this paper, we consider the safety of continuous time control systems with input delays. Safety functionals are constructed that define safety sets in the infinite-dimensional state space. Time-discretization is used in order to compute safety sets in finite dimensions and it is shown that these sets approach an infinite-dimensional safety set as the time step is decreased. A simple example of a nonlinear scalar system is used to demonstrate the convergence of the proposed methods.