An alternative approach to modelling and analysis of interactions among agents in multiagent systems (MAS) and their control is presented in analytical terms. The reachability graph of the Petri net (PN)-based model of MAS is found as well as the space of feasible states. Trajectories representing the interaction processes among agents in MAS are computed by means of the mutual intersection of both the straight-lined reachability tree (from a given initial state towards the terminal one) and the backtracking reachability tree (from the desired terminal state towards the initial one however, oriented towards the terminal state). Control interferences are obtained on base of the most suitable trajectory chosen from the set of feasible ones.