Adaptive control of a simple nonlinear system without a priori information on the plant parameters

The authors present an adaptive control scheme for nonlinear systems of the form x=c*^Tf(x)+b*u, where f(x) is Lipschitz, c* is a constant vector, and b* is a constant scalar. The control scheme achieves asymptotical model matching without a priori knowledge of the sign of the b* gain. The adaptive scheme is free from singularities in the sense that the estimate of b*, entering in the denominator of the control law, is bounded away from zero. The singularity has been overcome through a suitable modification of the parameter estimates which is based on standard least squares covariance matrix properties