A robust adaptive direct controller for dealing with non-linear first order systems

We present new results on designing a robust adaptive direct controller for a class of nonlinear first order systems, based on the use of a dead zone in the parameter update law. It is shown that the size of the dead zone does not depend on the upper bounds of the disturbances. However, in the ideal case of exogenous signal function and the function represents unmodeled dynamics of the systems equal to zero, the proposed controller does not mean the convergence to zero of the tracking error. Computer simulation results show the effectiveness of the controller in dealing with the stated problems.