سیم اچ پی ان : یک جعبه ابزار مت لپ برای شبیه سازی، تجزیه و تحلیل و طراحی با شبکه های هیبرید پتری

This paper presents a MATLAB embedded package for hybrid Petri nets called SimHPN. It offers a collection of tools devoted to simulation, analysis and synthesis of dynamical systems modeled by hybrid Petri nets. The package supports several server semantics for the firing of both, discrete and continuous, types of transitions. Besides providing different simulation options, SimHPN offers the possibility of computing steady state throughput bounds for continuous nets. For such a class of nets, optimal control and observability algorithms are also implemented. The package is fully integrated in MATLAB which allows the creation of powerful algebraic, statistical and graphical instruments that exploit the routines available in MATLAB.

Petri nets (PNs) [1] and [2] is a mathematical formalism for the description of discrete-event systems, that has been successfully used for modeling, analysis and synthesis purposes of such systems. A key feature of a PN is that its structure can capture graphically fundamental primitives in concurrency theory such as parallelism, synchronization, mutual exclusion, etc. The state of a PN system is given by a vector of non-negative integers representing the marking of its places. As any other formalism for discrete event systems, PNs suffer from the state explosion problem which produces an exponential growth of the size of the state space with respect to the initial marking. One way to avoid the state explosion is to relax the integrality constraint in the firing of transitions and deal with transitions that are fired in real amounts. A transition whose firing amount is allowed to be any real number between zero and its enabling degree is said to be a continuous transition. The firing of a continuous transition can produce a real, not integer, number of tokens in its input and output places. If all transitions of a net are continuous, then the net is said to be continuous. If a non-empty proper subset of transitions is continuous, then the net is said to be hybrid [3]. Different time interpretations can be considered for the firing of continuous transitions. The most popular ones are infinite and finite server semantics which represent a first order approximation of the firing frequency of discrete transitions. For a broad class of Petri nets, infinite server semantics offer a better approximation of the steady-state throughput than finite server semantics [4]. Moreover, finite server semantics can be exactly mimicked by infinite server semantics in discrete transitions simply by adding a self-loop place. A third firing semantics, called product semantics, is also frequently used when dealing with biochemical and population dynamics systems. In this paper, we present a new MATLAB embedded software called SimHPN that provides support for infinite server and product semantics in both, discrete and continuous, types of transition. A description of a preliminary version of this software can be found in [5] and [6]. As far as we know, this is the first MATLAB package that enables the analysis and simulation of hybrid nets with these two firing semantics. There already exists a toolbox dealing with discrete Petri nets [7], and one for the so-called first order hybrid Petri nets [8] which provides support for continuous transitions under finite server semantics. The main features of the SimHPN toolbox are (i) simulation of hybrid Petri nets under different server semantics; (ii) computation of steady state throughput bounds; (iii) computation of minimal P–T semiflows; (iv) optimal sensor placement; (v) optimal control algorithm; (vi) import models from different graphical Petri net editors. The paper is organized as follows. Section 2 introduces the formal definition of the hybrid Petri nets supported by SimHPN. Section 3 briefly presents the main features of the package. Sections 4, 5 and 6 exemplify those features by applying them to three case studies. Section 7 concludes the paper.

This paper has presented a new MATLAB package, called SimHPN, that allows us to perform several analysis and synthesis tasks on hybrid Petri nets working under different server semantics. In particular, SimHPN provides procedures to compute minimal P and T-semiflows, throughput bounds, optimal steady state and optimal sensor placement. Additionally, SimHPN is able of simulating hybrid Petri nets evolving under infinite server and product semantics. The package is equipped with a Graphical User Interface that offers a friendly interaction with the user.