This paper presents a novel data-driven method for learning deep constrained continuous control policies and dynamical models of the controlled system. By leveraging partial knowledge of system dynamics and constraint enforcing multi-objective loss functions, the method can learn from small and static datasets, handle time-varying state and input constraints and enforce the stability properties of the controlled system.We use a continuous control design example to demonstrate the performance of the method on three distinct tasks: system identification, control policy learning, and simultaneous system identification and policy learning.