An Application of the DEDS Control Synthesis Method

Abstract

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].

Synthesis of the Supervising Agent in MAS

“…Its nodes are the states reachable from the initial state x 0 and its edges are weighted by corresponding PN transitions enabling the state-to-state transit. The control synthesis based on RG is described in the author's works [3,5]. Consequently, this problem is not discussed here.…”

“…Namely, the ability to express the states of agents, the ability to test properties by means of the PN invariants and the reachability graph (RG) as well as the ability to synthesize the supervisory controllers by means of the invariants and RG [3,5] utilizing linear algebra predestinate PN to be frequently used. The model has the form as follows…”

Modelling, Analyzing and Control of Interactions Among Agents in MAS

“…The inputs of the procedure are the matrices F, G T and the initial state vector x 0 . The DEDS control synthesis based on the simple idea was also presented in [8]: (i) developing the straight-lined reachability tree (SLRT) from the given initial state x 0 towards the prescribed terminal state x t ; (ii) developing the backtracking reachability tree (BTRT) from x t towards x 0 however, directed to x t ; (iii) intersecting both the SLRT and BTRT. All of the steps are performed numerically in Matlab.…”

“…In [8] the Matlab procedure enumerating the (n RT × n RT )-dimensional quasifunctional adjacency matrix A of the RG and the space of the reachable states in the form of the (n×n RT )-dimensional matrix X reach was presented. The matrices fully characterize the RG.…”

“…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.…”