  This paper presents extensions of finite-time stability results to some
prototypical adaptive control and estimation frameworks. First, we present a
novel scheme of online parameter estimation that guarantees convergence of the
estimation error in a fixed time under a relaxed persistence of excitation
condition. Subsequently, we design a novel Model Reference Adaptive Control
(MRAC) for a scalar system with finite-time convergence guarantees for both the
state- and the parameter-error. Lastly, for a general class of strict-feedback
systems with unknown parameters, we propose a finite-time stabilizing control
based on adaptive backstepping techniques. We also present some numerical
examples demonstrating the efficacy of our scheme.
