In this thesis the consensus and formation problems of the multi-agent systems is investigated in presence of another interaction differ from communication links among the agents, that can be named as physical interaction or physical coupling. physical interaction between the agents usually occurs in the cases such as coordination, collaboration and cooperative in the multi-agent systems tasks. this physical interaction or physical coupling usually have adverse and negative impact on the consensus and accurate formation of the system. communication links and physcial couplings between the agents of the multi-agent system, are modeled by two distinct grpah layers, named communication graph and physical coupling graph, which may create similar or completely dissimilar physical and communication neighborhoods. here we intent to eliminate the adverse impacts of the physical coupling by using a fuzzy compensator in the multi-agent structure so that the group of agents be able to organize the desired formation without error. then by implemanting the proposed structure for eliminate the adverse impacts of the physical coupling on a quadrator multi-agent system, and locating the fuzzy compensator in the loop that added to the formation control, eliminate the physical coupling and provide formation for the system. also to achieving appropriate and proper formation and to decrease formation time of the system with nonlinear or not considered dynamics such as quadrator system, we use particle swarm optimization algorithm to optimize or tune the compensator outputs and formation control coefficients. english keywords: multi-agent systems , intelligent control , physical coupling , foramtion , consensus , graph