  Although persistent excitation is often acknowledged as a sufficient
condition to exponentially converge in the field of adaptive parameter
estimation, it must be noted that in practical applications this may be
unguaranteed. Recently, more attention has turned to another relaxed condition,
i.e., finite excitation. In this paper, for a class of nominal nonlinear
systems with unknown constant parameters, a novel method that combines the
Newton algorithm and the time-varying factor is proposed, which can achieve
exponential convergence under finite excitation. First, by introducing
pre-filtering, the nominal system is transformed to a linear parameterized
form. Then the detailed mathematical derivation is outlined from an estimation
error accumulated cost function. And it is given that the theoretical analysis
of the proposed method in stability and robustness. Finally, comparative
numerical simulations are given to illustrate the superiority of the proposed
method.
