Predictor-based safety control for systems with multiple time-varying delays

Abstract

Control barrier functions (CBFs) have been recently considered for ensuring safety of nonlinear input-affine systems by means of appropriately designed controllers rendering a desired superlevel set of the CBF function forward invariant. In this work, we consider the safety control problem for nonlinear input-affine systems with multiple time-varying input delays. In order to ensure safety, we first design a set of predictors that estimate the state of the system at different future times by utilizing the control laws designed to ensure safety of the delay-free system. Under the assumption of perfect estimation of the future states, we show that under the designed controller, the closed-loop performance of the systems with and without the input delays is the same by the time the input with the largest delay acts on the system with delays for the first time.