A simple robust adaptive control scheme for model reference adaptive control systems with nonlinear delayed state perturbations

The problem of model reference adaptive control (MRAC) is considered for a class of uncertain dynamical systems with nonlinear delayed state perturbations. It is assumed that the delayed state perturbations are nonlinear and that the time-varying delays are any nonnegative continuous and bounded functions which do not require that their derivatives have to be less than one. In particular, it is only assumed that the nonlinear delayed state perturbations are bounded in any nonnegative nonlinear functions which are also not required to be known for the system designer. For such a class of uncertain nonlinear time-delay MRAC systems, a new method is presented whereby a class of continuous memoryless robust adaptive controllers with a rather simpler structure is proposed. It is also shown that the proposed robust adaptive control schemes can guarantee that the current state of uncertain time-delay dynamical systems can track the state of a given delay-free reference model as far as possible, in the presence of the nonlinear delayed state perturbations.