Control Of Continuous Petri Nets Research Articles

Decentralised control of continuous Petri nets

ABSTRACTThis paper focuses on decentralised control of systems modelled by continuous Petri nets, in which a target marking control problem is discussed. In some previous works, an efficient ON/OFF strategy-based minimum-time controller was developed. Nevertheless, the convergence is only proved for subclasses like Choice-Free nets. For a general net, the pre-conditions of applying the ON/OFF strategy are not given; therefore, the application scope of the method is unclear. In this work, we provide two sufficient conditions of applying the ON/OFF strategy-based controller to general nets. Furthermore, an extended algorithm for general nets is proposed, in which control laws are computed based on some limited information, without knowing the detailed structure of subsystems.

ON/OFF strategy based minimum-time control of continuous Petri nets

This paper focuses on the target marking control problem of timed continuous Petri nets (TCPN), aiming to drive the system from an initial state to a desired final one. This problem is similar to the set-point control problem in a general continuous-state system. In a previous work, a simple and efficient ON/OFF controller was proposed for Choice-Free nets, and it was proved to be minimum-time (Wang, 2010). However, for general TCPN the ON/OFF controller may bring the system to “blocking” situations due to its “greedy” firing strategy, and the convergence to the final state is not ensured. In this work the ON/OFF controller is extended to general TCPN by adding more “fair” strategies to solve conflicts in the system: the ON/OFF+ controller is obtained by forcing proportional firings of conflicting transitions. Nevertheless, such kind of controller might highly slow down the system when transitions have flows of different orders of magnitude, therefore a balancing process is introduced, leading to the B-ON/OFF controller. A third approach introduced here is the MPC-ON/OFF controller, a combination of Model Predictive Control (MPC) and the ON/OFF strategy; it may achieve a smaller number of time steps for reaching the final states, but usually requires more CPU time for computing the control laws. All the proposed extensions are heuristic methods for the minimum-time control and their convergences are proved. Finally, an application example of a manufacturing cell is considered to illustrate the methods. It is shown that by using the proposed controllers, reasonable numbers of time steps for reaching the final state can be obtained with low computational complexity.

Guest editorial: hybrid systems, part II

We consider it a great privilege to introduce this two-part issue on Hybrid Systems to Discrete Event Dynamic Systems: Theory and Applications. Hybrid dynamical systems constitute an abstract modeling framework for systems with bi-layer dynamics: time-driven dynamics at the lower layer, and discrete-event dynamics at the upper layer. This framework provides useful analysis techniques and simulation tools for planning and control of systems in several application areas such as mobile robotics, automotive powertrains, switching circuits, manufacturing, and telecommunications. Consequently, hybrid systems have been extensively investigated by our research community, with emphases on the problems of stability, observability, control, and optimization. The hybrid-systems framework is diverse and includes linear and nonlinear models, deterministic and stochastic systems, and centralized systems as well as distributed networks. One of their unifying themes is the bi-level structure of their dynamics, and the exploration of the interactions between their time-driven dynamics and discrete-event dynamics has been a focus of extensive research. The purpose of this special issue is to bring together papers representing some of the main standing problems in the area of hybrid systems. The contributions comprising the first part of the special issue are summarized in the following paragraphs. The first paper in this issue, On Fluidization of Discrete Event Models: Observation and Control of Continuous Petri Nets, by M. Silva, J. Julvez, C. Mahulea, and C.R. Vazquez, provides a survey of hybrid Petri networks. It starts with a tutorial on the broad topic of fluidization of discrete event dynamic systems and its use in circumventing the problem of the state-space explosion. It then considers Petri networks in detail, where it describes how fluid and hybrid models can be used in

Control of continuous Petri nets using ON/OFF based method

Continuous Petri Nets (CPN) can be used to approximate classical discrete Petri nets which suffer from the state explosion problem. In this paper we focus on the control of timed CPN (TCPN), aiming to drive the system from an initial state to a desired final one. This problem is similar to the set-point control problem in a general continuous-state system. In a previous work, a simple and efficient ON/OFF controller was proposed for structurally persistent nets, and it is proved to be minimum-time. In this work the ON/OFF controller is extended to general TCPN, but in this case, the minimum-time evolution is not guaranteed. Two extensions are proposed, both of them are based on the ON/OFF strategy. Some comparisons of different control methods are given in terms of their applications to an assembly system.

On fluidization of discrete event models: observation and control of continuous Petri nets

As a preliminary overview, this work provides first a broad tutorial on the fluidization of discrete event dynamic models, an efficient technique for dealing with the classical state explosion problem. Even if named as continuous or fluid, the relaxed models obtained are frequently hybrid in a technical sense. Thus, there is plenty of room for using discrete, hybrid and continuous model techniques for logical verification, performance evaluation and control studies. Moreover, the possibilities for transferring concepts and techniques from one modeling paradigm to others are very significant, so there is much space for synergy. As a central modeling paradigm for parallel and synchronized discrete event systems, Petri nets (PNs) are then considered in much more detail. In this sense, this paper is somewhat complementary to David and Alla (2010). Our presentation of fluid views or approximations of PNs has sometimes a flavor of a survey, but also introduces some new ideas or techniques. Among the aspects that distinguish the adopted approach are: the focus on the relationships between discrete and continuous PN models, both for untimed, i.e., fully non-deterministic abstractions, and timed versions; the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory. After discussing observability and controllability issues, the most technical part in this work, the paper concludes with some remarks and possible directions for future research.

An Efficient Heuristics for Minimum Time Control of Continuous Petri nets

Abstract This paper considers the problem of controlling timed continuous Petri nets under infinite server semantics. The proposed control strategy assigns piecewise constant flows to transitions in order to reach the target state. First, by using linear programming, a method driving the system from the initial to the target state through a linear trajectory is developed. Then, in order to improve the time of the trajectory, intermediate states are added by means of bilinear programming.