This article presents a model-based hybrid adaptive dynamic programming (ADP) framework consisting of continuous feedback-based policy evaluation and policy improvement steps as well as an intermittent policy implementation procedure. This results in an intermittent ADP with a quantifiable performance and guaranteed closed-loop stability of the equilibrium point. To investigate the effect of aperiodic sampling on the communication bandwidth and the control performance of the intermittent ADP algorithms, we use a Hamiltonian-driven unified framework. With such a framework, it is shown that there is a tradeoff between the communication burden and the control performance. We finally show that the developed policies exhibit Zeno-free behaviors. Simulation examples show the efficiency of the proposed framework along with quantifiable comparisons of the policies with different intermittent information.