Modelling and Control of Discrete Event Dynamic Systems

Abstract

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.

Modelling, Analyzing and Control of Interactions Among Agents in MAS

“…PN marking was denoted here by the letter x usually denoting the state in system theory. Fuzzy PN [10] can be modelled analogically -see [2]. Higher-level PN models usually cannot be expressed in such a pure analytical form although they are advantageous as to the smaller dimensionality.…”

“….., n expresses very analogically the causal relations among the discrete events (causes) and the DEDS states (consequences); the structural matrix B is given by means of the arcs incidence matrices F and G according to (2); (.) T symbolizes the matrix or vector transposition.…”

The Generalised Method for Solving Problems of the DEDS Control Synthesis

“…To avoid problems with computer handling ∆ k two simple approaches to control synthesis were proposed. The first of them published in [2,3,4] is based on ODG and the second one presented in [5] is based on BDG.…”

“…The author has published in [2,3,4] the method suitable for SM -the special class of OPN -where each transition has only one input place and only one output place. The control synthesis method utilizing directed graphs (DG) was developed there for such a kind of DEDS.…”