<p>This paper proceeds from professional learning community for graduate students that promotes individual growth as well as team growth. The professional learning community is characterized of asymmetric study willingness, which means that study among community members is not necessarily bidirectional, but can also be unidirectional. But there is a research gap in the modeling of asymmetric study willingness. Development of general artificial intelligence provides some implications for the research of professional learning community, and this paper introduces a CAIDD (Continuous Action Iterated Double-layer Dilemma) model to simulate the asymmetric study willingness of community members. Within the professional learning community, crucial members can better facilitate the communication network and improve the group dynamics of the community. So we divide the communication network within the professional learning community into two layers and put forwards a double-layer communication network. Teacher leaders form the upper layer while graduate students form the second layer of the network. To improve the effectiveness, a guiding mechanism of LQR(linear quadratic regulator) is introduced to guide the upper layer of teachers. The Lyapunov function is designed to prove the effectiveness of the proposed model and the guiding mechanism. And this is complemented by an in-depth discussion.</p>