Adaptive control scheme for uncertain time-delay systems

The paper exposes some of the potential of a recently introduced backstepping transformation for linear uncertain time-delay systems to address the classic problems of equilibrium regulation under partial measurements, disturbance rejection, parameter or delay adaptation. For each of these problems, an implementable control strategy is proposed. It is analyzed through a convergence analysis of infinite dimensional dynamics, based on a transport partial differential equation representation of the estimated input delay and the mentioned backstepping transformation. The considered controllers contain this representation of the system, under the form of a distributed parameter system, and use it to determine relevant adaptation strategies. An illustration example is proposed.