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Petri Net Supervisor Synthesis on a Class of Finite Forbidden State Specifications

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Tutor: ZuoJian SuHongYe WuWeiMin
School: Zhejiang University
Course: Control Theory and Engineering
Keywords: Supervisory Control,Discrete Event Systems,Petri Nets,Input Dominant Petri Nets,
CLC: TM571.6
Type: Master's thesis
Year:  2005
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A discrete event system (DES) is a dynamic system that evolves in accordance with the abrupt occurrence of events, at possibly unknown irregular intervals. Its application involves a number of man-made systems, such as flexible manufacturing systems, large scale computer networks and communication networks, vehicular traffic management systems, C3/ military command systems, etc. In logical aspects, its models include finite state machine and Petri nets. Since compared with finite state machjne, Petri nets have such advantages as a higher language complexity, a compact and graphical description of the state space and the ability of synthesis in a modular way, we adopt Petri nets as our analyzing and synthesizing tool.Usually we should control DES¡¯s behavior to meet special specifications, like preventing the system from special states, especially deadlock. Such problem is called forbidden state problem and is the main concern of this thesis.We propose transformation function based synthesis method and state feedback based synthesis method so as to deal with finite, arbitrary forbidden state problems, especially when the forbidden states can not be expressed as linear inequality constraints using existing methods. In the transformation function based method, we propose reverse net analysis to compute weakly forbidden marking (WFM) set without constructing influence paths. Through introducing transformation function, which facilitates not only constructing monitor places but also synthesizing controllers, we obtain maximally permissive supervisors. The method need not analyze reachability graph and its online computation has only a complexity of polynomial times. More importantly, the method can be applied to more general Petri nets than existing similar methods.In state feedback based method, reverse net analysis is used not only in computing WFM, but also in synthesizing controllers. Therefore we propose the concept of critical marking-transition tuple. We notice that the controlled net may include deadlocks caused by the introduction of control policy. The problem is rarely studied and we propose a deadlock-free supervisor synthesis method on bounded Petri nets.Inspired by transformation function, we propose constraint function to cope with OR constraints of several linear inequalities. Then we give Place Invariant method more intuitive meaning using function construction based method and propose one placestructure (OPS), which consists of a place and arcs connecting the place with transitions in plant net, to show that the structure can only realize linear constraints and it is invalid for nonlinear ones.While studying supervisory control, we have explored Petri nets theory too. We propose two special classes of Petri nets, i.e., Input Dominant Petri nets and Output Dominant Petri nets, all of which are a superset of state machines. In addition, we propose an unbounded Petri net analysis approach based on reduced modified reachability tree (RMRT) so as to improve the deficient deadlock theorem obtained from modified reachability tree based approach. The RMRT based approach provides further background for deadlock research using reachability tree.
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