In the present work, we consider a System Optimum Dynamic Traffic Assignment optimization problem on road networks employing time-varying partial traffic flow control. Depending on the network performance, trajectory control between the relative origin and destination nodes is applied to a variable fraction ("compliant") of the demand. Network dynamics is derived by applying a Godunov discretization of the well-known Lightwill-Williams-Richards model, where the fundamental flow-density diagram is of the triangular form. At each node, a multi-class priority-based solver handles flow routing according to an aggregate class-density weighted distribution matrix coupled with a priority vector associated to incoming links. The selfish response of the uncontrolled fraction of flows ("non-compliant") is addressed by updating the class-specific distribution matrices according to changing traffic conditions and consistently with a multinomial Logit random choice model. The goal of the the partial control optimization problem is to globally improve the network congestion level by rerouting a variable fraction of flows over a set of pre-computed routes. The fraction of controlled users varies according to the trade-off between the rerouting effort and the network status improvement. Results on a synthetic network are then presented and discussed.