Universal adaptive control of feedforward time-delay systems with lower- and higher-order non-linearities

This study considers a class of high-order feedforward non-linear time-delay systems with lower- and higher-order non-linearities. Owing to the upper-triangular structure, backstepping-like methods are in general not applicable. To overcome this difficulty, the authors introduce a dynamic gain scaling transformation and construct a novel dynamic gain that is used to compensate the unknown parameter in the sense of universal adaptive control. With the help of the adding a power integrator technique and the Lyapunov-Krasovskii theorem, a delay-independent controller with a novel dynamic gain is explicitly constructed under the condition of less conservative assumption, to globally asymptotically regulate all states of origin system to zero as time goes to infinity while guaranteeing that the dynamic gain is uniformly bounded. Finally, an illustrative example is given to show the usefulness of the proposed design method.