Results 1  10
of
29
On observability in timed continuous Petri net systems
 In: Proc. of the 1st Int. Conf. on Quantitative Evaluation of Systems (QEST) 2004. Twente, The Netherlands
, 2004
"... Abstract – The design of observers is a topic of major importance in systems theory. Under a given firing semantics for transitions, the formalism of timed continuous Petri net systems represents a specific kind of piecewise linear system: the linear system that drives the evolution of the net syste ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
(Show Context)
Abstract – The design of observers is a topic of major importance in systems theory. Under a given firing semantics for transitions, the formalism of timed continuous Petri net systems represents a specific kind of piecewise linear system: the linear system that drives the evolution of the net system depends exclusively on the marking. This implies that a switch occurs only when an internal event happens. This paper deals with observability on continuous Petri nets and focuses on the design of observers. The proposed observers are piecewise linear systems that assure the continuity of the estimate even when a switch occurs. The use of the system simulation may allow to estimate even the unobservable space of the net system during a given time period.
Optimal model predictive control of Timed Continuous Petri nets
, 2007
"... This paper addresses the optimal control problem of timed continuous Petri nets under infinite servers semantics. In particular, our goal is to find a control input optimizing a certain cost function that permits the evolution from an initial marking (state) to a desired steadystate. The solution w ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
This paper addresses the optimal control problem of timed continuous Petri nets under infinite servers semantics. In particular, our goal is to find a control input optimizing a certain cost function that permits the evolution from an initial marking (state) to a desired steadystate. The solution we propose is based on a particular discretetime representation of the controlled continuous Petri net system, as a certain linear constrained system. An upper bound on the sample period is given in order to preserve important information of the timed continuous net, in particular the positiveness of the markings. The reachability space of the sampled system in relation to autonomous continuous Petri nets is also studied. Based on the resulting linear constrained model, the optimal control problem is studied through Model Predictive Control (MPC). Implicit and explicit procedures are presented together with a comparison between the two schemes. Stability of the closedloop system is also studied.
Basic Server Semantics and Performance Monotonicity of Continuous Petri Nets
, 2008
"... Continuous Petri nets were introduced as an approximation to deal with the state explosion problem which can appear in discrete event models. When time is introduced, the flow through a fluidified transition can be defined in many ways. The most used in literature are constant and variable speed [8] ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
Continuous Petri nets were introduced as an approximation to deal with the state explosion problem which can appear in discrete event models. When time is introduced, the flow through a fluidified transition can be defined in many ways. The most used in literature are constant and variable speed [8], which can be seen as some kind of finite and infinite server interpretations of the transitions behavior, and derived from stochastic (discrete) Petri nets [18]. In this paper we will compare the results obtained with both relaxations for the broad class of monoTsemiflow reducible nets, and prove that, under some frequently true conditions, infinite server semantics offers a throughput which is closer to the throughput of the discrete system in steady state. In the second part, it will be proved that the throughput of monoTsemiflow reducible net systems is monotone with respect to the speed of the transitions and the initial marking of the net.
Continuization of Timed Petri Nets: From Performance Evaluation to Observation and Control
 In Proc. of the 26th Int. Conf. On Application and Theory of Petri Nets and Other Models of Concurrency
, 2005
"... Abstract. State explosion is a fundamental problem in the analysis and synthesis of discrete event systems. Continuous Petri nets can be seen as a relaxation of discrete models allowing more efficient (in some cases polynomial time) analysis and synthesis algorithms. Nevertheless computational costs ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
(Show Context)
Abstract. State explosion is a fundamental problem in the analysis and synthesis of discrete event systems. Continuous Petri nets can be seen as a relaxation of discrete models allowing more efficient (in some cases polynomial time) analysis and synthesis algorithms. Nevertheless computational costs can be reduced at the expense of the analyzability of some properties. Even more, some net systems do not allow any kind of continuization. The present work first considers these aspects and some of the alternative formalisms usable for continuous relaxations of discrete systems. Particular emphasis is done later on the presentation of some results concerning performance evaluation, parametric design and marking (i.e., state) observation and control. Even if a significant amount of results are available today for continuous net systems, many essential issues are still not solved. A list of some of these are given in the introduction as an invitation to work on them. 1
Steady State Control, Zero Valued Poles and Token Conservation Laws in Continuous Net Systems
, 2005
"... The control problem for continuous Petri nets under infinite server semantics is approached in this paper. First, some characterizations of equilibrium points in steadystate are given. Being piecewise linear systems, for every linear system we present results that will characterize the possible ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
The control problem for continuous Petri nets under infinite server semantics is approached in this paper. First, some characterizations of equilibrium points in steadystate are given. Being piecewise linear systems, for every linear system we present results that will characterize the possible steadystates. Second, optimal control for steadystate is studied, a problem that surprisingly can be computed in polynomial time, when all transitions are controlfeasible. Third, an interpretation of controllability aspects in the framework of linear dynamic system is presented.
Optimal Observability For Continuous Petri Nets
 In 16 IFAC World Congress
, 2005
"... Optimal observability of continuous Petri Nets consists in deciding the places to be measured (considering that all are measurable) such that the net system is observable and a cost function is minimal. Unfortunately this is not a simple covering problem. The results obtained in the paper are use ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
(Show Context)
Optimal observability of continuous Petri Nets consists in deciding the places to be measured (considering that all are measurable) such that the net system is observable and a cost function is minimal. Unfortunately this is not a simple covering problem. The results obtained in the paper are used in the implementation of an algorithm to improve the pure combinatorial search.
Optimal control of timed continuous Petri nets via explicit MPC
 In Proc. of 2 nd Multidisciplinary International Symposium on Positive Systems: Theory and Applications, Lecture Notes in Control and Information Sciences
, 2006
"... Abstract. In this paper we deal with the problem of controlling timed continuous Petri nets in order to reach a nal (steady state) con guration while minimizing a quadratic performance index. The formulation of a discretetime linear positive model with dynamic (or statebased) constraints on the co ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we deal with the problem of controlling timed continuous Petri nets in order to reach a nal (steady state) con guration while minimizing a quadratic performance index. The formulation of a discretetime linear positive model with dynamic (or statebased) constraints on the control input, enables us to design a statefeedback control law based on explicit model predictive control (eMPC). The eMPC partitions the state space into polytopes: an a ne statefeedback control law is uniquely associated to each polytope, while the online phase of the approach consists in evaluating the current region and consequently the optimal control law. 1
Hybrid Petri net model of a traffic intersection in a urban network
"... Abstract — Control in urban traffic networks constitutes an important and challenging research topic nowadays. In the literature, a lot of work can be found devoted to improving the performance of the traffic flow in such systems, by means of controlling the redtogreen switching times of traffic s ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Abstract — Control in urban traffic networks constitutes an important and challenging research topic nowadays. In the literature, a lot of work can be found devoted to improving the performance of the traffic flow in such systems, by means of controlling the redtogreen switching times of traffic signals. Different techniques have been proposed and commercially implemented, ranging from heuristic methods to modelbased optimization. However, given the complexity of the dynamics and the scale of urban traffic networks, there is still a lot of scope for improvement. In this work, a new hybrid model for the traffic behavior at an intersection is introduced. It captures important aspects of the flow dynamics in urban networks. It is shown how this model can be used in order to obtain control strategies that improve the flow of traffic at intersections, leading to the future possibility of controlling several connected intersections in a distributed way. I.
Giua: Linear programming techniques for analysis and control of batches Petri nets
 10th International Workshop on Discrete Event Systems
"... In this paper we consider Generalised Batches Petri nets (GBPN) and develop new linear algebraic techniques for the analysis of this model. Two main contributions are presented. The first contribution lies in the fact that although we consider the same GBPN model that has already be presented in the ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
In this paper we consider Generalised Batches Petri nets (GBPN) and develop new linear algebraic techniques for the analysis of this model. Two main contributions are presented. The first contribution lies in the fact that although we consider the same GBPN model that has already be presented in the literature, we associate to this model a different semantics considering that the instantaneous firing flow of continuous and batch transitions are control variables that can take an arbitrary value provided they satisfy given constraints. The second contribution consists in the analysis of the steady state behavior of GBPN. We show that under the assumption that no discrete transition fires, a steady state can be characterized by solving a linear programming problem that takes into account the net structure and the initial marking. Published as: I. Demongodin, A. Giua, "Linear programming techniques for analysis and con
Improving analysis and simulation of continuous Petri nets
 In 2 nd IEEE Conference on Automation Science and Engineering
, 2006
"... Abstract — State explosion problems in the analysis of discrete event dynamic systems have lead to relaxed views, fluidification in particular. Proceeding in that way continuous Petri nets have been defined. For infinite servers semantics, switching linear systems appear through the presence of mini ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract — State explosion problems in the analysis of discrete event dynamic systems have lead to relaxed views, fluidification in particular. Proceeding in that way continuous Petri nets have been defined. For infinite servers semantics, switching linear systems appear through the presence of minimum operators due to synchronizations. The analysis of the ODEs defining the semantics of those hybrid models suffers from two problems: the existence of the minimum operators and stiffness. In discrete models, an approximated way to deal with stiffness was to classify the transitions into immediate and timed (thus markings are divided into vanishing and tangible). Avoiding synchronizations (hence minimum operators) and removing immediate transitions at net level becomes a crucial issue for continuous Petri nets because timed continuous net models and ODEs are isomorphous. The application to an example taken from the literature illustrates our purpose and the computational advantages obtained. Index Terms — Continuous Petri nets, immediate transitions, improving simulation