  We attempt to constrain the kinematics of the thin and thick disks using the
Besancon population synthesis model together with RAVE DR4 and Gaia first data
release (TGAS). The RAVE fields were simulated by applying a detailed target
selection function and the kinematics was computed using velocity ellipsoids
depending on age in order to study the secular evolution. We accounted for the
asymmetric drift computed from fitting a Stackel potential to orbits. Model
parameters such as velocity dispersions, mean motions, and velocity gradients
were adjusted using an ABC-MCMC method. We made use of the metallicity to
enhance the separation between thin and thick disks. We show that this model is
able to reproduce the kinematics of the local disks in great detail. The disk
follows the expected secular evolution, in very good agreement with previous
studies of the thin disk. The new asymmetric drift formula, fitted to our
previously described St\"ackel potential, fairly well reproduces the velocity
distribution in a wide solar neighborhood. The U and W components of the solar
motion determined with this method agree well with previous studies. However,
we find a smaller V component than previously thought, essentially because we
include the variation of the asymmetric drift with distance to the plane. The
thick disk is represented by a long period of formation (at least 2 Gyr),
during which, as we show, the mean velocity increases with time while the scale
height and scale length decrease, very consistently with a collapse phase with
conservation of angular momentum. This new Galactic dynamical model is able to
reproduce the observed velocities in a wide solar neighborhood at the quality
level of the TGAS-RAVE sample, allowing us to constrain the thin and thick disk
dynamical evolution, as well as determining the solar motion.
