  In a Hilbert setting, for convex differentiable optimization, we develop a
general framework for adaptive accelerated gradient methods. They are based on
damped inertial dynamics where the coefficients are designed in a closed-loop
way. Specifically, the damping is a feedback control of the velocity, or of the
gradient of the objective function. For this, we develop a closed-loop version
of the time scaling and averaging technique introduced by the authors. We thus
obtain autonomous inertial dynamics which involve vanishing viscous damping and
implicit Hessian driven damping. By simply using the convergence rates for the
continuous steepest descent and Jensen's inequality, without the need for
further Lyapunov analysis, we show that the trajectories have several
remarkable properties at once: they ensure fast convergence of values, fast
convergence of the gradients towards zero, and they converge to optimal
solutions. Our approach leads to parallel algorithmic results, that we study in
the case of proximal algorithms. These are among the very first general results
of this type obtained using autonomous dynamics.
