Discretization-Robust Safety Barrier of Partial Differential Equation

This paper presents a method for ensuring the safety of a system governed by partial differential equation (PDE). Our approach is to spatially discretize the PDE to obtain an ordinary differential equation (ODE) that approximates the system behavior with a known maximal approximation error. A safe controller is subsequently designed for the ODE using control barrier function while taking the approximation error into account. The framework is verified on the control of a flexible beam modeled as an Euler-Bernoulli beam. The designed controller is verified in a simulation of a simple motion that exemplifies a scenario of remote maintenance of the DEMO fusion power plant.