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Abstract. 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 straightlined 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.

An application of the method suitable for modelling and control of general discrete event dynamic systems (DEDS) to special kinds of communication systems is presented in this paper. The approach is based on Petri nets (PN) defined in [12] and directed graphs (DG) described in [11]. It is supported by the previous author's works [1]-[10], [13].

The method represents a generalisation of the author's method presented recently. It extends the validity of the original method to the wider class of discrete-event dynamic systems (DEDS) to be controlled. Both the original method and the innovated one are suitable for DEDS able to be described by ordinary Petri nets (OPN). The earlier method can be successfully used only in case of the DEDS described by the special class of OPN -so called state machines (SM). The method proposed here can be used in case of DEDS described by the bounded OPN. While SM have special restrictions on their structure the bounded OPN have no structural restrictions. Namely, SM are OPN with transitions having only the single input place and the single output place. Thus, the validity of the method is extended because the class of bounded OPN is undoubtedly many times wider than the class of OPN represented by SM. Both the original method and the proposed one can alternatively utilize ordinary directed graphs (ODG) or bipartite directed graphs (BDG).

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A new control synthesis method suitable for a special kind of discrete event dynamic systems (DEDS) is presented in this paper. The systems to be controlled are modelled by a special class of Petri nets (PN) named state machine (SM). The class is distinctive by the fact that each PN transition has only one input place and only one output place. Bipartite directed graphs (BDG) are utilized in the control synthesis process. Namely, PN in general are (from the structure point of view) the BDG. Both the state reachability tree and the corresponding control one are developed in the straight‐line procedure starting from the given initial state and directed to the desirable terminal one as well as in the backtracking procedure starting from the terminal state and directed to the initial one. After a suitable intersection of both the straight‐lined state reachability tree and the backtracking one the state trajectories of the system are obtained. After the intersection of both the straight‐lined control reachability tree and the backtracking one the control interferences corresponding to the state trajectories are obtained.

Discrete event dynamic systems (DEDS) in general are <br />investigated as to their analytical models most suitable for control<br />purposes and as to the analytical methods of the control synthesis.<br /> The possibility of utilising both the selected kind of Petri nets<br />and the oriented graphs on this way is pointed out. Because many<br />times the control task specifications (like criteria, constraints, <br />special demands, etc.) are given only verbally or in another form of<br />non analytical terms, a suitable knowledge representation about<br />the specifications is needed. Special kinds of Petri nets (logical,<br />fuzzy) are suitable on this way too. Hence, the knowledge-based<br />control synthesis of DEDS can also be examined. The developed<br />graphical tools for model drawing and testing as well as for the<br />automated knowledge-based control synthesis are described and<br />illustratively presented.<br />Two approaches to modelling and control synthesis based on<br />oriented graphs are developed. They are suitable when the <br />system model is described by the special kind of Petri nets - state<br />machines. At the control synthesis the first of them is straightforward<br /> while the second one combines both the straight-lined model<br />dynamics development (starting from the given initial state <br />towards the prescribed terminal one) and the backtracking model<br />dynamics development.