Direct Adaptive Control for Nonlinear Uncertain Systems with Time Delay

A direct adaptive control framework for nonlinear uncertain delay dynamical systems is developed. The proposed framework is Lyapunov-Krasovskii-based and guarantees asymptotic stability with respect to the plant states. Specifically, if the nonlinear system is represented in normal form, then it is shown that nonlinear adaptive controllers can be constructed without requiring knowledge of the system dynamics except the system delay amount. Furthermore, in the case where the system is particularly given in a multivariable second-order form, the adaptive control law is shown to be simplified and constructed without even requiring the information of the delay amount. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach. Copyright c © 2005 IFAC