By Christos G. Cassandras
ISBN-10: 1475740700
ISBN-13: 9781475740707
ISBN-10: 1475740727
ISBN-13: 9781475740721
Introduction to Discrete occasion structures is a finished creation to the sector of discrete occasion platforms, supplying a breadth of insurance that makes the fabric available to readers of various backgrounds. The ebook emphasizes a unified modeling framework that transcends particular program parts, linking the subsequent issues in a coherent demeanour: language and automata thought, supervisory keep an eye on, Petri web conception, Markov chains and queuing conception, discrete-event simulation, and concurrent estimation recommendations. This variation contains contemporary study effects bearing on the prognosis of discrete occasion structures, decentralized supervisory keep watch over, and interval-based timed automata and hybrid automata models.
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Extra resources for Introduction to Discrete Event Systems
Sample text
34) The sequence of time instants when UI (t) = 1 defines the "schedule" of product arrivals at the warehouse. Similarly, the sequence of time instants when U2(t) = 1 defines the "schedule" of truck arrivals at the warehouse. It is interesting to observe the similarity between the tank flow system of Fig. 8, and the warehouse system illustrated in Fig. 12. In both cases, we study the level of a storage container of some type, subject to specified inflow and outflow processes. The difference is in the nature of what is being stored: A fluid level is accurately measured through a real variable, whereas the level of an inventory of discrete entities requires an integer-valued state variable.
The state of this system is the position of the particle, (Xl,X2), measured on a plane, with Xt,X2 taking only integer values, that is, the state space is the discrete set X = {(i,j) : i,j = ... , -1,0,1, ... }. In this case, a natural event set is E = {N, S, W, E} corresponding to the four events "one step north", "one step south", "one step west", and "one step east". Fig. 20 shows a sample path in the (Xl, X2) space (as in Fig. 10) resulting from an initial state (0,0) and the sequence of events {E, S, W, W, N, N, W}.
20) is discontinuous at points in time such that x(t) = 0 or x(t) = K: the value of x(t) jumps to 0 at such points. Remark. It is tempting to claim that all dynamic systems can be modeled through differential equations, no matter how nonlinear and complex they might be. Although it is certainly true that these models are immensely useful in system and control theory, we will soon see that for the discrete event systems we need to consider, differential equations simply do not capture the essential dynamic behavior, or they lead to design and control solutions that are not sufficiently accurate for many practical purposes.