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^*T f(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 parameters estimates which is based on standard least squares covariance matrix properties