Safety-Critical Control of Systems with Time-Varying Input Delay

In this paper, we describe an approach for designing safety-critical controllers for nonlinear systems with time-varying input delay. This approach involves combining a safe, control barrier function (CBF) based feedback law for the nominal delay-free system with a state predictor that compensates the time-varying input delay. We show that under predictor-feedback, a safe feedback law designed for the nominal system achieves the same closed-loop safety properties for the input-delayed system, provided the system remains safe before the controller kicks in. We include two numerical examples that illustrate the effectiveness of our approach.