Augmented Adaptive Observer for a Differentiable Regressor

We show that constructing an augmented adaptive observer, where the extended state is a mix of the original states and their derivatives, we can enhance the transient performance and obtain robust estimation results for the original state and the unknown parameters. The convergence of the proposed augmented adaptive observer is shown under the persistence of excitation assumption by constructing a Lyapunov function and using the input-to-output stability framework. The performance of the design is illustrated via numerical simulations.