Automated Solving of the DEDS Control Problems

Systems Analysis Modelling Simulation

2002

A new view on the control synthesis of DEDS (discrete event dynamic systems) is presented in this paper. Petri nets (PN), frequently used for DEDS modelling, are understood here in a form of corresponding oriented graphs (OG) where the nodes of the OG are represented by the PN positions and the OG edges involve the PN transitions. The adjacency matrix of such a graph (or better said its transpose) is utilized in the DEDS control synthesis procedure. It is used for generating the numerical form of the state reachability tree in both the case of the straight-lined system development (from a given initial state to a prescribed terminal one) and that of the backtracking one (from the prescribed terminal state to the initial one). A suitable combination of both the straight-lined development of the OG-based model and the backtracking one is used in order to perform the DEDS control synthesis. Namely, the coincidence both of the reachability trees yields possible trajectories of the system development. Corresponding sequences of the control discrete events are found just by means of the OG adjacency matrix.

Section: The Development Of the K-invariant System Dynamicsmentioning

confidence: 99%

Section: The Deds Control Synthesis Problem and Its Solutionmentioning

confidence: 99%

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A Solution of DEDS Control Synthesis Problems

Systems Analysis Modelling Simulation

2002

“…SM can be understood to be the DG with the PN places being the DG nodes and the PN transitions being fixed to the DG edges. Hence, the SM state reachability tree can be developed (Cˇapkovicˇ, 1999) as followsEquation 1where k is the discrete step (the level of the tree); x ( k )=( σ p 1 ( k ) ( γ ),…, σ p n ( k ) ( γ )) T , k =0, N is the n ‐dimensional state vector in the step k ; σ p i ( k ) ( γ ), i =1, n is the state of the elementary place p i in the step k . It depends on actual enabling its input transitions.…”

Section: Introductionmentioning

confidence: 99%

Control synthesis of a class of DEDS

2002

Kybernetes

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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.

“…In addition to this the nodes are marked in order to express dynamics development. The SM reachability tree (RT) was developed in [1] as follows…”

Section: The Principle Of the Original Methodsmentioning

confidence: 99%

The Generalised Method for Solving Problems of the DEDS Control Synthesis

Developments in Applied Artificial Intelligence

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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).