Cooperative Control Approach for Library Group Therapy with Constraint Conditions

In this paper, group therapy behavior is studied from the viewpoint of cooperative control. To describe the range of emotional changes in each participant, nonconvex constraint sets are employed, which can be used to quantitatively represent the differences among all the participants. Then, a cooperative control model is proposed to describe the interaction between participants. Based on this model, emotion analysis is performed, and it is shown that all participants finally reach an emotion consensus regardless of facilitators being involved. In particular, when facilitators are absent, the final states of all participants cannot be controlled, while when facilitators are involved, the final states of all participants can be driven to a desired state of mental health. Numerical simulation examples are given to illustrate the theoretical conclusions.