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.