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A bslract-Thls paper addresses the observabillty problem In Dlscretc Event Systems modeled by lnterpreted Petrl N e t ( I P N ) . The concepts of Input and output sequence lnvarlants of an IPN are Introduced. These sequence Invariants are used t o state a ehareeterlzatlon of observable I P N , arhleh Is slmllar t o the one presented for continuos systems using e geometrlc approach. However, slnce the eomputatlon of sequence lnvarlants Is eomputatlonaly herd, the charaetsrlzatlon of observable I P N Using sequence lnvarlants Is turned Into e charactsrlzatlon based on the notlons of event-detectablllty and marklngdetectablllty.Kevwods-Observablllty, Sequence Invariants, EventDeteetablllty, Marklng-Dstectablllty, Interpreted Petrl Nets, Dlrcrete Event Systems. IYTRODUCTIONObservability is an important property of dynamic syst,ems since it, implies t,he possibility of estimating t . h m system statcs t h a t cannot. be directly meosurcd. Observability is defined in linear cont.inuous systems as the possibility of determining t.he init.ial state of the system inafinitetime by usingthe knowledgeofthesystem inputs, outputs and structure 121.In the Discrete Event Systems (DES) area, some definitions of observability has been proposed. Most of those definitions have been st,ated in regular language t e r m , where the concept of observability has been t.id t.o the supervisor existence problem. For example, M. Wonham 1111 studies t.he obserxability problem from t,he supervisory control point using Finite State Machines (FShf) under partial event observations: a language K is observable, if the information provided by the observed event sequence suffices t o compute a control law such that the syst,em is constrained to I<. This notion of observability has been extended by several aurhors in order t o solve the dist,rihuted and decent,ralized controller design problem under partial observat.ions, [i], [9]. However, in most of the previous works: the exact computation of the system state is not addrrxsed.In the frame of the Petri Net (J'.V) formalism, Ichikawa and Hiraishi [(i] divide the observability problem into two subproblems: fir&, to cnmpiit.e t,he sequence of eveut. occurrences given a sequence of stat.e observations; and sccondly, t,o coinputc a set of possible initial states given the sequence of event. Occurrences. Based on event observations, Giua and Seatzu [5] provide several notions of observability such as marking, uniform and struct.ura1 observabilitifs, which are related to the exidenre of event sequence that lead the estimat,ion error to zero. On the other hand, k i n g t,he Interpreted Petri Net (IPN) formalism, Aguirre et. al. 111 introduce a notion of observability b a s e d on full event, observation and provide a characterization of obser5able I P X . Rivera et al. [SI provide a notion of observable IPN under partial event aiid slate observations and a procedure for designing observers. This paper studies the observability property from the IPN approach. Herein, it, is s s u m e d that. t,he DES is mo...

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This paper deals with supervisory control of Discrete Event Systems (DES) modeled by Interpreted Petri Nets (IPN). In the approach herein proposed, both, the specification and the system model are described by IPN, however, the specification describes a state subset that the specification must reach. It also captures the order in which these states must be reached. Based on this framework, this paper presents a method to compute the system firing transition sequence in order to confine the system model into the specification behavior. Although this problem is NP-complete, the proposed solution exploits the structural information of both IPN (system and specification) to compute Parikh vectors of system firing sequences; one vector per each transition of the specification. These Parikh vectors are processed in order to obtain controllable fireable transition sequences. Thus a divide and conquer technique is used, where the NP-complete problem divided into k small size problems (where k is the number of specification transitions), reducing the computational time of proposed algorithms. Moreover, the technique herein presented is suitable for distributed and hierarchical control. All algorithms herein purposed have being implemented in MAPLE.

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This paper addresses the asymptotic observer design problem in discrete event systems modeled by live, cyclic and conservative Interpreted Petri Nets ( I P N ) . A procedure for constructing asymptotic observers is provided. The observer convergency analysis is based on the observer estimation error, which is also represented as an IF", resulting in a fast convergency ratio.