Simple adaptive robust control schemes of uncertain strict-feedback non-linear time-delay systems

The main purpose of this study is to present a simple design method to synthesise the adaptive robust controllers for a class of uncertain strict-feedback non-linear systems with delayed state perturbations and external disturbances. In this study, such a simple design method is presented so that (i) the presented design method is easy to understand for the system designers; (ii) it is not necessary to know any information on the upper bound functions of non-linear delayed state perturbations and the non-linear functions due to the derivatives of the fictitious control functions to construct some state feedback control schemes; and (iii) the resulting adaptive robust control schemes are simple and easy to implement in practical engineering control problems. The adaptive robust controllers synthesised by the presented design method have a rather simple structure, and can guarantee the uniform exponential boundedness of the considered uncertain strict-feedback non-linear time-delay systems. A numerical example is provided to illustrate the authors' simple design procedure and the corresponding simulations are made to demonstrate the validity of the theoretical results.