Direct Adaptive Control for Nonlinear Uncertain Systems with Time Delay

A direct adaptive control framework for nonlinear uncertain delaydynamical systems is developed. The proposed framework isLyapunov-Krasovskii-based and guarantees asymptotic stability withrespect to the plant states. Specifically, if the nonlinear systemis represented in normal form, then it is shown that nonlinearadaptive controllers can be constructed without requiring knowledgeof the system dynamics except the system delay amount. Furthermore,in the case where the system is particularly given in amultivariable second-order form, the adaptive control law is shownto be simplified and constructed without even requiring the information of thedelay amount. Finally, a numerical example is provided todemonstrate the efficacy of the proposed approach.