Parameter estimation and control for a class of systems with nonlinear parametrization

We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show that under this restriction standard persistent excitation suffices to ensure exponentially fast convergence of the estimates to the actual values of unknown parameters. Subsequently, our approach is extended to cases in which the monotonicity assumption holds only locally. We show that excitation with high-frequency of oscillations is sufficient to ensure convergence. Two practically relevant examples are given in order to illustrate the effectiveness of the approach.