  Gradient algorithms are classical in adaptive control and parameter
estimation. For instantaneous quadratic cost functions they lead to a linear
time-varying dynamic system that converges exponentially under persistence of
excitation conditions. In this paper we consider (instantaneous) non-quadratic
cost functions, for which the gradient algorithm leads to non-linear (and non
Lipschitz) time-varying dynamics, which are homogeneous in the state. We show
that under persistence of excitation conditions they also converge globally,
uniformly and asymptotically. Compared to the linear counterpart, they
accelerate the convergence and can provide for finite-time or fixed-time
stability.
