Dynamics and steady state analysis of controlled Generalized Batches Petri Nets

This paper is dedicated to an extended class of hybrid Petri nets called controlled Generalized Batches Petri Nets. The novel feature of these nets is that the firing flow of continuous and batch transitions and the transfer speed of batch places are control variables. First we propose a linear programming problem to compute the instantaneous firing flow vector and the instantaneous transfer speed vector solving an optimization problem, where the objective function depends on the control goal. Second we analyze and characterize the steady state of this model solving a programming problem that takes into account the net structure and the initial marking. This problem is linear if the transfer speeds are preassigned while it is nonlinear if the transfer speeds are control variables. In such a last case, a viable technique to compute a family of solutions by linear relaxation of the non linear problem is presented. The optimality of steady states for given linear objective functions is also addressed

Stationary behavior of controlled Generalised Batches Petri Nets

In this paper we consider controlled Generalised Batches Petri Nets, a class of batches nets where the firing flow of continuous and batch transitions and the transfer speed of batch places are control variables to be selected within an admissible range. We show that the steady state behavior of this class of nets during a period in which no discrete transition fires can be characterized by solving a nonlinear programming problem that takes into account the net structure and the initial marking. A viable technique to compute a family of solutions by linear relaxation is also presented

ON/OFF Control Trajectory Computation for Steady State Reaching in Batches Petri Nets

International audienc

Testing experiments on bounded Petri nets

Synchronizing sequences have been proposed in the late 1960s to solve testing problems on systems modeled by finite-state machines. Such sequences lead a system, seen as a black box, from an unknown current state to a known final one. This paper presents a first investigation of the computation of synchronizing sequences for systems modeled by synchronized Petri nets. In the first part of the paper, existing techniques for automata are adapted to this new setting. Later on, new approaches, that exploit the net structure to efficiently compute synchronizing sequences without an exhaustive enumeration of the state space, are presented. Note to Practitioners: Driving a system to a known state when its current state is not known is a very important problem in many practical applications, such as checking communication protocols, part orienteers, digital reset circuit, etc. This topic has received a lot of attention in the past few decades. The classic approach to solve this problem considers systems modeled by automata. In particular, a standard technique requires the computation of a synchronizing sequence, i.e., a sequence of inputs that drives the system to a unique final state independently of the initial state and does not require the observation of the system's outputs. This paper presents a first investigation on the computation of synchronizing sequences for systems modeled by synchronized Petri nets. Petri nets are a very intuitive model that is widely used in automation. Many analysis problems can be efficiently solved using Petri nets by taking into account the net structure, without an exhaustive enumeration of its state space. The techniques we propose for computing synchronizing sequences exploit the net structure and lead to viable algorithms that can be applied to large scale systems

Synchronizing sequences on a class of unbounded systems using synchronized Petri nets

Determining the state of a system when one does not know its current initial state is a very important problem in many practical applications as checking communication protocols, part orienteers, digital circuit reset, etc. Synchronizing sequences have been proposed in the 60’s to solve the problem on systems modeled by finite state machines. This paper presents a first investigation of the synchronizing problem on unbounded systems, using synchronized Petri nets, i.e., nets whose evolution is driven by external input events. The proposed approach suffers from the fact that no finite space representation can exhaustively answer to the reachability problem but we show that synchronizing sequences may be computed for a particular class of unbounded synchronized Petri nets

Synchronizing Sequences On Not Strongly Connected Petri Nets

In testing Discrete Event System, an important topic is determining the final state of the machine after the application of a test. Synchronizing and homing sequences have been proposed in the sixties to solve the problem using Mealy machines. A synchronizing sequence drives an implementation of a given model, seen as a black box, to a known state regardless of its initial state and the outputs. In this paper, we investigate how to determine synchronizing sequences using systems represented by a class of synchronized Petri nets. We propose an approach that can be applied to (not necessarily strongly) connected nets. Regardless of the number of tokens that the net contains, a synchronizing sequence may be computed in terms of the net structure, thus avoiding the state explosion problem