Aims. We attempt to constrain the kinematics of the thin and thick disks using the Besançon population synthesis model together with RAVE DR4 and Gaia first data release (TGAS).Methods. 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 Stäckel 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.Results. 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 Stäckel 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. Conclusions. 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.