Observability in interpreted Petri nets using sequence invariants

Abstract

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...

Observability analysis of interpreted Petri nets under partial state observations using estimations reachability graph

“…Sequence-detectability implies the knowledge of all ring sequences of an IP N , thus the problem of determining whether or not a system is sequence-detectable has a high computational complexity. However, testing a system for event-detectability, a stronger property, allows to overcome this complexity, [1].…”

“…This paper uses the concepts introduced in [1] and [8] to provide a procedure to obtain the estimations reachability graph of an IP N under partial state observations given an initial output signal. The graph is constructed under the following assumptions: 1) the initial marking is unknown, 2) the structure of the IP N is known, 3) the total number of tokens contained in the net and their distribution is known but their exact location is unknown, 4) Every transition ring can be detected immediately after its occurrence and before another transition res.…”

Fault Diagnosis in Discrete Event Systems Using Interpreted Petri Nets

“…Roughly speaking, this property says that an IPN is diagnosable if it is possible to know both, when a faulty place is marked and which faulty place is marked. This property is closely related to the observability property (Aguirre-Salas, et al, 2002) and and polynomial algorithms to test when an IPN is diagnosable are derived, avoiding the reachability analysis of other approaches. Also, a distributed diagnoser is presented; every distributed diagnoser uses the local information or communication among diagnosers for detecting and locating a system fault.…”