Dans ce cas, la matrice A peutêtreécrite sous la forme d'une matrice diagonale par bloc, après une permutation de lignes et de colonnes ,
, La permutation des lignes de la matrice A peutêtre formalisée comme la multiplicatio? a gauche de la matrice A par la matrice de permutation P , qui est la matrice d'identité ayant des lignes réordonnées. Alors, le polyèdre A.x un ? b est décrit comme suit : P.A
, la matrice A par la matrice de permutation Q, qui est la matrice d'identité ayant des colonnes réordonnées. En outre, la permutation des colonnes de A conduità une permutation des variables de x un (permutation des lignes de x un ). Par conséquent, cette permutation conduità la multiplicationà gauche de x un par la matrice de permutation Q . Comme Q = Q ?1 (une propriété des matrices de permutation)
,
Robust fault tolerant tracking controller design for vehicle dynamics : A descriptor approach. mechatronics, vol.30, pp.316-326, 2015. ,
A determinizable class of timed automata, International Conference on Computer Aided Verification, pp.1-13, 1994. ,
Surveillance des systèmesàévénements discrets commandés : Conception et implémentation en utilisant l'automate programmable industriel, 2008. ,
Bw analysis : a backward reachability analysis for diagnostic problem solving suitable to parallel implementation, International Conference on Application and Theory of Petri Nets, pp.39-58, 1994. ,
Complexity issues in coding theory, 1997. ,
On structural analysis of interacting behavioral petri nets for distributed causal model-based diagnosis, International Journal of Foundations of Computer Science, vol.23, issue.07, pp.1523-1541, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-01126346
A novel model repair approach of timed discrete-event systems with anomalies, IEEE Transactions on Automation Science and Engineering, vol.13, issue.4, pp.1541-1556, 2016. ,
Fault diagnosis using timed automata, International Conference on Foundations of Software Science and Computation Structures, pp.219-233, 2005. ,
An efficient approach for online diagnosis of discrete event systems, IEEE Transactions on Automatic Control, vol.54, issue.4, pp.748-759, 2009. ,
State estimation and fault diagnosis of time labeled petri net systems with unobservable transitions, IEEE Trans. Autom. Control, pp.997-1009, 2014. ,
Linear matrix inequalities in system and control theory, vol.15, 1994. ,
Algebraic coding theory, 2015. ,
Diagnosis of asynchronous discrete-event systems : a net unfolding approach, IEEE Transactions on Automatic Control, vol.48, issue.5, pp.714-727, 2003. ,
URL : https://hal.archives-ouvertes.fr/inria-00072442
Distributed contextual diagnosis for very large systems, 2004. ,
Bernard Riera, et al. Identification of discrete event systems using ordinary petri nets, DX'17-28th International Workshop on Principles of Diagnosis, vol.11, p.8, 2006. ,
A recurrence for counting graphical partitions. the electronic journal of combinatorics, vol.2, p.11, 1995. ,
Efficient generation of graphical partitions, Discrete applied mathematics, vol.78, issue.1-3, pp.17-26, 1997. ,
Coloured petri nets for chronicle recognition, International Conference on Reliable Software Technologies, pp.266-281, 2009. ,
Diagnosis using an estimation method for partially observed petri net, 20th World Congress of the International Federation of Automatic Control (IFAC), vol.50, 2017. ,
Diagnostic based on estimation using linear programming for partially observable petri nets with indistinguishable events, International Journal of Systems Science : Operations & Logistics, pp.1-14, 2018. ,
,
Linear algebraic formalism for state estimation of labeled petri net, 17th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), pp.717-722, 2016. ,
Discrete event diagnosis using labeled petri nets. an application to manufacturing systems, Control Engineering Practice, vol.19, issue.9, pp.989-1001, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-01479645
Marking estimation of petri nets with silent transitions, Decision and Control, 2004. CDC. 43rd IEEE Conference on, vol.1, pp.966-971, 2004. ,
Diagnosis using labeled petri nets : faults may either be silent or undistinguishable events, Proc. IEEE Conference on Automation Science and Engineering, 2010. ,
Fault detection for discrete event systems using petri nets with unobservable transitions, Automatica, vol.46, issue.9, pp.1531-1539, 2010. ,
Diagnosis using labeled petri nets with silent or undistinguishable fault events, IEEE Transactions on Systems, Man, and Cybernetics : Systems, vol.43, issue.2, pp.345-355, 2013. ,
Marking observer in labeled petri nets with application to supervisory control, IEEE Transactions on Automatic Control, vol.62, issue.4, pp.1813-1824, 2017. ,
Diagnosis of partially observed petri net based on analytical redundancy relationships, Asian Journal of Control, vol.21, issue.5, pp.1-14, 2019. ,
Introductionà l'algorithmique, 1997. ,
Du grafcet aux réseaux de petri. traité des nouvelles technologies, série automatique, 1989. ,
Fourier-motzkin elimination and its dual, 1972. ,
State estimation of timed labeled petri nets with unobservable transitions, IEEE Transactions on Automation Science and Engineering, vol.11, issue.1, pp.103-110, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01003990
State estimation of timed labeled petri nets with unobservable transitions, IEEE Transactions on Automation Science and Engineering, vol.11, issue.1, pp.103-110, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01003990
Fault detection of discrete event systems using petri nets and integer linear programming, IFAC Proceedings Volumes, vol.41, pp.6554-6559, 2008. ,
On-line fault detection in discrete event systems by petri nets and integer linear programming, Automatica, vol.45, issue.11, pp.2665-2672, 2009. ,
Distributed diagnosis for large discrete event dynamic systems, Proc of the IFAC congress, 2002. ,
The minimal coverability graph for petri nets, International Conference on Application and Theory of Petri Nets, pp.210-243, 1991. ,
Fault detection by labeled petri nets and time constraints, Dependable Control of Discrete Systems (DCDS), pp.168-173, 2011. ,
Fault detection by labeled petri nets in centralized and distributed approaches, IEEE Transactions on Automation Science and Engineering, vol.10, issue.2, pp.392-404, 2013. ,
State estimation of ?-free labeled petri nets with contact-free nondeterministic transitions ,
, Discrete Event Dynamic Systems, vol.15, issue.1, pp.85-108, 2005.
Consensus-based decentralized supervision of petri nets, Decision and Control and European Control Conference (CDC-ECC), pp.1128-1135, 2011. ,
Distributed diagnosis of discreteevent systems using petri nets, International Conference on Application and Theory of Petri Nets, pp.316-336, 2003. ,
Fault diagnosis with coloured petri nets using latent nestling method, Industrial Electronics, vol.4, pp.986-991, 2007. ,
A systems theory view of petri nets ,
, Advances in control theory and applications, pp.99-127, 2007.
A monitoring approach for discrete events systems based on a time petri net model, Proc. of 16th IFAC world congress, pp.5-15, 2005. ,
State observer for des under partial observation with time petri nets, Discrete Event Dynamic Systems, vol.19, issue.2, pp.137-165, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00801148
Bayesian sensor fault detection in a markov jump system, Asian Journal of Control, vol.19, issue.4, pp.1465-1481, 2017. ,
Partition of a graph into cycles and vertices ,
, Discrete Mathematics, vol.307, issue.11, pp.1436-1440, 2007.
Monitoring discrete event systems using petri net embeddings, International Conference on Application and Theory of Petri Nets, pp.188-207, 1999. ,
Decentralized supervision of petri nets. Supervisory Control of Concurrent Systems : A Petri Net Structural Approach, pp.93-123, 2006. ,
About redundant inequalities generated by fourier's algorithm, Artificial Intelligence IV, pp.117-127, 1990. ,
Fourier's elimination : Which to choose ? In PPCP, pp.117-129, 1993. ,
Contextual analysis of petri nets for distributed applications, 16th Int. Symp. on Mathematical Theory of Networks and Systems, vol.135, p.136, 2004. ,
A distributed approach for fault detection and diagnosis based on time petri nets, Mathematics and Computers in Simulation, vol.70, issue.5-6, pp.287-313, 2006. ,
On-line monitoring of large petri net models under partial observation, Discrete Event Dynamic Systems, vol.18, issue.3, pp.323-354, 2008. ,
Projections of convex polyhedral sets, 1967. ,
Solvability and consistency for linear equations and inequalities, The American Mathematical Monthly, vol.63, issue.4, pp.217-232, 1956. ,
Diagnostic observer design for t-s fuzzy systems : Application to real-time-weighted fault-detection approach, IEEE Transactions on Fuzzy Systems, vol.26, issue.2, pp.805-816, 2018. ,
Diagnosis of des with petri net models, IEEE Transactions on Automation Science and Engineering, vol.4, issue.1, pp.114-118, 2007. ,
Diagnosis with petri nets according to partial events and states observation, IFAC Proceedings Volumes, vol.45, pp.1244-1249, 2012. ,
On-line fault diagnosis with partially observed petri nets, IEEE Transactions on Automatic Control, vol.59, issue.7, pp.1919-1924, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01966537
On-the-fly and incremental technique for fault diagnosis of discrete event systems modeled by labeled petri nets, Asian Journal of Control, vol.19, issue.5, pp.1659-1671, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01463809
Least-cost transition firing sequence estimation in labeled petri nets with unobservable transitions ,
, IEEE Transactions on Automation Science and Engineering, vol.8, issue.2, pp.394-403, 2011.
Non-blocking decentralized control of discrete event systems based on petri nets, Asian Journal of Control, vol.12, issue.3, pp.323-335, 2010. ,
Diagnostic, reconstruction et identification des dé-fauts capteurs et actionneurs : application aux station d'épurations des eaux usées, 2012. ,
Fault diagnosis of discrete-event systems using continuous petri nets, IEEE Transactions on Systems, Man, and Cybernetics-Part A : Systems and Humans, vol.42, issue.4, pp.970-984, 2012. ,
Petri nets : Properties, analysis and applications. Proceedings of the IEEE, vol.77, pp.541-580, 1989. ,
Un cas remarquable de systèmes linéaires : les systèmes monotones Résolution et applicationà la vérification formelle de programmes, 2001. ,
Model dynamique et signature du défaut inter-spires intermittent dans les têtes de bobines d'une msap, Symposium de Genie Electrique, 2016. ,
Computing the block triangular form of a sparse matrix, ACM Transactions on Mathematical Software (TOMS), vol.16, issue.4, pp.303-324, 1990. ,
Fault diagnosis based on petri net reduced models, Electrical and Electronics Engineering, pp.1-5, 2006. ,
State estimation in discrete event systems modeled by labeled petri nets, Decision and Control, 2006. ,
, 45th IEEE Conference on, pp.6022-6027, 2006.
Bounds on the number of markings consistent with label observations in petri nets, IEEE Transactions on Automation Science and Engineering, vol.6, issue.2, pp.334-344, 2009. ,
Fault diagnosis in discrete event systems modeled by partially observed petri nets, Discrete Event Dynamic Systems, vol.19, issue.4, p.551, 2009. ,
Minimal communication in a distributed discrete-event control system, American Control Conference, vol.3, pp.1965-1970, 1999. ,
, IEEE, 1999.
Identification and Fault Diagnosis of Industrial Closedloop Discrete Event Systems : Identifikation und Fehlerdiagnose Industrieller Ereignisdiskreter Closed-Loop-Systeme, 2010. ,
Structural diagnosability of des and design of reduced petri net diagnosers, IEEE Transactions on Systems, Man, and Cybernetics-Part A : Systems and Humans, vol.42, pp.416-429, 2012. ,
Fault diagnosis for discrete event systems modeled by bounded petri nets ,
, Asian Journal of Control, vol.19, issue.4, pp.1532-1541, 2017.
Structuring acyclic petri nets for reachability analysis and control, Discrete Event Dynamic Systems, vol.12, issue.1, pp.7-41, 2002. ,
Theory of linear and integer programming, 1998. ,
Fault detection/monitoring using time petri nets, IEEE transactions on systems, man, and cybernetics, vol.23, pp.1155-1162, 1993. ,
Decentralized fault free model approach for fault detection and isolation of discrete event systems, European Journal of Control, vol.18, issue.1, pp.82-93, 2012. ,
Decentralized diagnosis based on boolean discrete event models : application on manufacturing systems, International journal of production research, vol.46, issue.19, pp.5469-5490, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-02111221
Coverability graphs for a class of synchronously executed unbounded petri net, Journal of Parallel and Distributed Computing, vol.10, issue.3, pp.253-260, 1990. ,
Consistency's checking of chronicles' set using time petri nets, Control & Automation (MED), 2010 18th Mediterranean Conference on, pp.1520-1525 ,
, , 2010.
Algebraic approaches for fault identification in discrete-event systems, IEEE Transactions on Automatic Control, vol.50, issue.12, pp.2048-2055, 2005. ,
Advanced r. Chapman and Hall/CRC, 2014. ,
Distributed h8 consensus fault detection for uncertain t-s fuzzy systems with time-varying delays over lossy sensor networks, Asian Journal of Control, 2018. ,
Diagnosis of time petri nets using fault diagnosis graph, IEEE Transactions on Automatic Control, vol.60, issue.9, pp.2321-2335, 2015. ,
High level synthesis of data flow graphs using integer linear programming for switching power reduction, Signal Processing, Communication, Computing and Networking Technologies (ICSCCN), 2011 International Conference on, pp.475-479, 2011. ,
Contributionà la surveillance des systèmes de productionà l'aide des réseaux de neurones dynamiques : Applicationà la e-maintenance, 2003. ,
Basis marking representation of petri net reachability spaces and its application to the reachability problem, IEEE Transactions on Automatic Control, vol.62, issue.3, pp.1078-1093, 2017. ,
Fault detection and isolation method based on h-/h8 unknown input observer design in finite frequency domain, Asian Journal of Control, vol.19, issue.5, pp.1777-1790, 2017. ,