  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.
