Control synthesis of a class of DEDS

Abstract

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.

Petri net-based problem solving

“…The latter one allows to draw reachability graph and automatically find the trajectories from a given initial state to the prescribed terminal one. It utilizes intersection of two rechability trees [4]- [6]. Namely, the straight-lined reachability tree starting from the initial state developed towards the terminal one and the backward reachability tree starting from the terminal state and developed back towards the initial state.…”

“…The latter tool yields the possibility to draw RG and find all paths from the initial state (root node) to a prescribed terminal state (terminal node). GraSim utilizes the results achieved in [4]- [6], namely, the intersection of the straightlined RT (developed from the root node) and the backward RT developed back from the terminal node. Applying the experience and/or prescribed rules, constraints, limitations, etc., the infeasible paths can be eliminated.…”

Modelling systems by hypergraphs

“…Another approach, based on causal graph is presented by Gentil et al (2004). Čapkovič (2002) presents a new method of control synthesis of DEDS, where the system is a state machine synthesised as a bipartite graph. Sarkar and Sivarajan (1998) extend the use of graph‐theoretical methods to the field of hypergraphs and show that channel assignment in a 37‐cell system modelled by a hypergraph carries 30 percent more traffic than a system modelled by a simple graph.…”

Modelling, Analyzing and Control of Interactions Among Agents in MAS

“…PN were chosen to model MAS too [12], [11]. On the base of previous experience [3], [4], [7] with PN-based modelling and control synthesis of the discrete event dynamic systems (DEDS) and the agent cooperation [5], [6] a new approach to modelling, analysis and control of the negotiation process is proposed here. The negotiation process is understood to be DEDS.…”