Robust adaptive control scheme for uncertain non-linear model reference adaptive control systems with time-varying delays

The problem of model reference adaptive control is considered for a class of uncertain dynamical systems with non-linear delayed state perturbations. It is assumed that the time-varying delays are any non-negative continuous and bounded functions. In particular, it is only assumed that the non-linear delayed state perturbations are bounded in any non-negative non-linear functions which are not required to be known for the system designer. A new method is presented whereby a class of continuous memoryless robust adaptive controllers with a rather simple structure can be constructed. It is also shown that the proposed robust adaptive control schemes can guarantee that the current state of uncertain non-linear time-delay dynamical systems can track the state of a given delay-free reference model as far as possible. Finally, the simulations of a numerical example are provided to demonstrate the validity of the theoretical results.