  In this paper, a concurrent learning based adaptive observer is developed for
a class of second-order nonlinear time-invariant systems with uncertain
dynamics. The developed technique results in uniformly ultimately bounded state
and parameter estimation errors. As opposed to persistent excitation which is
required for parameter convergence in traditional adaptive control methods, the
developed technique only requires excitation over a finite time interval to
achieve parameter convergence. Simulation results in both noise-free and noisy
environments are presented to validate the design.
