Prediction-based control of linear systems subject to state-dependent state delay and multiple input-delays

This paper presents a prediction-based controller strategy for linear systems subject to a state-dependent state delay and distinct constant input delays. We propose to compute corresponding predictions in cascade and use them in a nominal control law obtained from the input-delays free case. Using transport Partial Differential Equation (PDE) reformulations and backstepping transformations, we show that this control law compensates for the input delays in closed loop and provides nominal exponential stabilization. The mechanisms of this technique are illustrated on the dynamics of the mechanical vibrations in drilling, which has recently been described as a cutting process.