The Generalised Method for Solving Problems of the DEDS Control Synthesis

Abstract

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).

A modular system approach to DES synthesis and control

“…In [7] the (N a × N a )-dimensional quasi-functional adjacency matrix q A k of the P/T PN reachability graph (RG) was mentioned. Its elements q a ij are integers expressing indices of the transitions connecting the RG nodes.…”

“…The (n × N a )-dimensional matrix X reach containing (as its columns) the PN reachable states (markings) X i , i = 1, · · · , N a , representing the nodes of the RG, was mentioned there as well. Both matrices are given on the output of the procedure (written in Matlab) introduced in [7], when the matrices F, G T and the initial state vector x 0 are given as its inputs.…”

An Application of the DEDS Control Synthesis Method

“…is the state of the elementary DG node π i in the step k. Its value depends on actual enabling its input transitions. γ symbolizes this dependency; In [1], [2] the procedure enumerating the quasi-functional adjacency matrix A of the RG and the space of the PN reachable states in the form of the matrix X reach was presented in a different depth. The columns of the matrix X reach are the PN state vectors x 0 , x 1 , x 2 , ... reachable from the initial state x 0 .…”

Modelling, Analyzing and Control of Interactions Among Agents in MAS

“…the situation when the agent A 1 is free and it is asked by the agent A 2 to solve the problem P B = P A2 . Using the algorithm introduced in [4] we have the following quasi-adjacency matrix A (its elements are the indices of the PN transitions) of the PN reachability tree and the matrix X reach with columns beeing the feasible states (the initial state and all states reachable from this initial state) PN-based model of the agent is universal and it can be used for modelling other agents of MAS too. Namely, the same interpretation of places (however with shifted numbering p i+12 , i = 1, ..., 12) can be used e.g for the agent A 2 .…”

“…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.…”