Adaptive control of time delay nonlinear systems with unknown control direction

In this paper, robust adaptive control is proposed for a class of time delay nonlinear systems with unknown constant control gain and control direction. The design is based on the principle of sliding mode control and the use of Nussbaum-type function in solving the problem of the completely unknown control gain. The unknown function and the upper bound of the unknown time delay term are assumed to be in the form of nonlinear functions with unknown coefficients. The uncertain time delay terms are compensated for using appropriate Lyapunov- Krasovskii functional and Young´s inequality in the design. The closed-loop control system is proved to be semi-globally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the approach.