Maxime Grangereau, Wim van Ackooij, and St{\'{e}}phane Gaubert.
Multi-stage stochastic alternating current optimal power flow with
storage: Bounding the relaxation gap.
Electric Power Systems Research, 206:107774, May 2022.
doi:10.1016/j.epsr.2022.107774>/A>
COVID-19 APHP-Universities-INRIA-INSERM Group, collective name for Frédéric
Adnet, Marin Boyet, Jean-Jacques Avrane, Frédéric Batteux, Pierre-Yves
Boëlle, Jérémie Boutet, Vincent Calvez, Pierre Carli, Pascal Chansard,
Charlotte Chollet, François Crémieux, Diane Descamps, Stéphane Gaubert,
Laurent Goix, Pierre Hausfater, Martin Hirsch, Eric Lecarpentier, Thomas
Loeb, Jean-Sébastien Marx, Catherine Paugam, Renaud Piarroux, Bruno Riou
(corresponding author), Remi Salomon, Caroline Telion, and Antoine
Vieillard-Baron.
Early indicators of intensive care unit bed
requirement during the COVID-19 epidemic: A
retrospective study in Ile-de-France region,
France, PLOS ONE, 2020,
doi:10.1371/journal.pone.0241406.
M. Akian, L. Ganassali, S. Gaubert, L. Massoulié,
Probabilistic and mean-field model of COVID-19 epidemics with user mobility and contact tracing, arXiv:2009.05304
Olivier Beaude, Pascal Benchimol, Stéphane Gaubert , Paulin Jacquot , and Nadia Oudjane,
A Privacy-Preserving Method to Optimize Distributed Resource Allocation,
SIAM J. Optim., 30(3), 2303--2336.
doi:10.1137/19M127879X
Marianne Akian, Xavier Allamigeon, Marin Boyet, Stéphane Gaubert,
A convex programming approach to solve posynomial systems,
Proceedings of the
International Congress on Mathematical Software 2020, TU Braunschweig, July 13-16, 2020, Bigatti, Anna Maria and Carette, Jacques and Davenport, James H. and Joswig, Michael and de Wolff, Timo, Eds, Lecture Notes in Computer Science, volume 12097, Springer, 2020
arXiv:2005.07124
Xavier Allamigeon, Marin Boyet, and Stéphane Gaubert,
Piecewise Affine Dynamical Models of Timed Petri Nets -- Application to Emergency Call Centers, Proceedings of the Petri Nets conference,
Paris, 2020, The extended version appeared in Fundamentae Informaticae,
183(3-4): 169--201 (2021), doi:10.3233/FI-2021-2086arXiv:2004.09483
Marianne Akian, Stéphane Gaubert, Zheng Qu, and Omar Saadi. Solving ergodic Markov decision
processes and perfect information zero-sum stochastic games by variance reduced deflated value iteration. In Proc. of the 58th IEEE Conference on Decision and Control, 2019.
arXiv:1909.06185
Paulin Jacquot, Olivier Beaude, Pascal Benchimol, Stéphane Gaubert, and Nadia Oudjane. A privacy-preserving disaggregation algorithm for non-intrusive management of flexible energy. In Proc. of the
58th IEEE Conference on Decision and Control, 2019.
arXiv:1903.03053
Giuseppe C. Calafiore, Stephane Gaubert and Corrado Possieri. A universal approximation
result for difference of log-sum-exp neural networks,
IEEE Trans Neural Networks Learn Syst. 2020 Dec;31(12):5603--5612.
doi:10.1109/TNNLS.2020.2975051arXiv:1905.08503
G. C. Calafiore, S. Gaubert, and C. Possieri.
Log-sum-exp neural networks and posynomial models for
convex and log-log-convex data. IEEE Transactions on Neural Networks and Learning Systems, pages
1--12, 2019. doi:10.1109/TNNLS.2019.2910417arXiv:1806.07850
S. Gaubert and M. McCaig,
Approximating the Volume of Tropical Polytopes is Difficult,
International Journal of Algebra and Computation Vol. 29, No. 02,
2019,
arXiv:1706.0646710.1142/S0218196719500061
X. Allamigeon, S. Gaubert, E. Goubault, S. Putot
and N. Stott. A fast method to compute disjunctive quadratic invariants of numerical programs, ACM Transactions on Embedded
Computing Systems (TECS), 16(5), 2017. Special Issue ESWEEK 2017, CASES 2017, CODES + ISSS
2017 and EMSOFT 2017, Seoul, South Korea.
doi:10.1145/3126502
J. Depersin, S. Gaubert, and M. Joswig.
A tropical isoperimetric inequality, Article 27, 12 pp, Séminaire
Lotharingien de Combinatoire, 78B, 2017, Proceedings of FPSAC 2017 (29th Conference on Formal Power Series and Algebraic Combinatorics, London)
arXiv:1611.04148
M. Akian, S. Gaubert, and A. Hochart.
Hypergraph conditions for the solvability of the ergodic equation for
zero-sum games.
Proceedings of the 55th IEEE Annual
Conference on Decision and Control (CDC), Osaka, 2015.
arXiv:1510.05396
[bib]
X. Allamigeon, S. Gaubert, E. Goubault, S. Putot
ad N. Stott. A scalable algebraic method to infer quadratic invariants of switched systems
In 2015 International Conference on
Embedded Software, EMSOFT 2015, Amsterdam, Netherlands, October 4-9, 2015, pages 75--84, 2015 (best paper award).
doi:10.1109/EMSOFT.2015.7318262 [bib]
An extended version of the present article has been published in
ACM Transactions on Embedded Computing Systems (TECS), Volume 15 Issue 4, August 2016,
doi:10.1145/2932187
S. Gaubert, Z. Qu, and S. Sridharan.
Maximizing concave piecewise affine functions on the unitary group.
Optimization Letters, 10:4, pp 655-665, 2016.
doi:10.1007/s11590-015-0951-y [bib]
S. Gaubert, Z. Qu, S. Sridharan,
Bundle-based pruning in the max-plus curse of dimensionality free method, arXiv:1402.1436. An abridged version of this paper has appeared in the
Proceedings of the 21st International Symposium on
Mathematical Theory of Networks and Systems,
July 7-11, 2014. Groningen, The Netherlands, pp. 166-172, [bib], [pdf]. Some of the materials here, completed with proofs, have been published in the journal
article immediately above.
M. Akian, S. Gaubert, A. Guterman,
Tropical Cramer Determinants Revisited,
In G.L. Litvinov and S.N. Sergeev, editors, Proceedings of the
International Conference on Tropical and Idempotent Mathematics, volume 616
of Contemporary Mathematics, pages 1–45. American Mathematical
Society, 2014.
arXiv:1309.6298.
[bib]
X. Allamigeon, S. Gaubert, V. Magron and B. Werner, Certification of Bounds of Non-linear Functions: the Templates Method , in Proceedings of CICM 2013 (Conferences on Intelligent Computer Mathematics, ``Calculemus'', Track A), Bath, July 8-12, 2013 arXiv:1307.3231. An improved and extended version has appeared in the journal article immediately above.
F. Billy, J. Clairambault, O. Fercoq, S. Gaubert, T. Lepoutre T. Ouillon, and S. Saitoh,
Synchronisation and control of proliferation in cycling cell population models with age structure,
Mathematics and Computers in Simulation, vol 96, pp. 66--94, 2014,
10.1016/j.matcom.2012.03.005, hal-00662885, [bib]
S. Gaubert and W. McEneaney. Min-max spaces and complexity reduction in min-max expansions. Appl. Math. Optim., 65(3):315--348, June 2012.
doi:10.1007/s00245-011-9158-5, [bib].
F. Billy, J. Clairambault, O. Fercoq, S. Gaubert, T. Lepoutre and T. Ouillon,
Proliferation in Cell Population Models with Age Structure,
AIP Conf. Proc., Volume 1389, pp. 1212--1215, 2011,
10.1063/1.3637834,
[bib].
T. M. Gawlitza, H. Seidl, A. Adje, S. Gaubert and E. Goubault,
Abstract interpretation meets convex optimization,
Journal of symbolic computation,
47(12):1416-1446, December 2012,
Special issue on invariant generation and advanced techniques for reasoning about loops, doi:10.1016/j.jsc.2011.12.048,
[bib].
S. Gaubert, R. Katz and S. Sergeev.
Tropical linear-fractional programming and parametric mean payoff games.
Journal of symbolic computation, volume 27, number 12, pages 1447-1478,
2012,
arXiv:1101.3431,
doi:10.1016/j.jsc.2011.12.049,
[bib].
Journal version of a communication to the
Third international Workshop on Invariant Generation (WING'2010), associated
with the International Joint Conference on Automated Reasoning (IJCAR 2010), Edinburgh July 21, 2010.
S. Gaubert, R. Katz, and S. Sergeev.
Tropical linear programming and parametric mean payoff games.
In Third international Workshop on Invariant Generation
(WING’2010), associated with the International Joint Conference on Automated
Reasoning (IJCAR 2010), Edinburgh July 21. 2010.
[pdf]. An extended version of the present work has
appeared in Journal of symbolic computation, volume 27, number 12, pages 1447-1478, 2012, see the bibliographic input above
(arXiv:1101.3431).
J. Edmonds, S. Gaubert, and V. Gurvich,
Sperner oiks,
Electronic Notes in Discrete Mathematics, 36:1273--1280, 2010.
Proceedings of ISCO 2010 - International Symposium on Combinatorial
Optimization, doi:10.1016/j.endm.2010.05.161
[bib].
J. Edmonds, S. Gaubert, and V. Gurvich.
Scarf oiks.
Electronic Notes in Discrete Mathematics, 36:1281--1288, 2010.
Proceedings of ISCO 2010 - International Symposium on Combinatorial
Optimization, doi:10.1016/j.endm.2010.05.162,
[bib].
M. Akian, S. Gaubert, and A. Guterman.
The correspondence between tropical convexity and mean payoff games, Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), 5-9 July, 2010, Budapest, Hungary, pp. 1295--1302, ISBN 978-963-311-370-7, [bib].
This is a conference paper announcing
the results of the paper immediately below (arXiv:0912.2462).
S. Gaubert.
Max-plus algebraic tools for discrete event systems, static analysis,
and zero sum games (extended abstract associated to an invited talk).
In J. Ouaknine and F. Vaandrager, editors, Formal Modeling and
Analysis of Timed Systems: 7th International Conference, FORMATS 2009,
volume 5813 of LNCS, pages 7--11, Springer, 2009,
doi:10.1007/978-3-642-04368-0_2, [bib].
X. Allamigeon, S. Gaubert and E. Goubault,
Computing the vertices of tropical polyhedra using directed
hypergraphs.
Discrete Comp. Geom., 49(2):247–279, 2013.
arXiv:0904.3436v3,
doi:10.1007/s00454-012-9469-6, [bib].
An announcement of the results of this paper appeared in STACS,
reference immediately above this one (arXiv:1001.4119).
M. Akian, S. Gaubert and V. Kolokoltsov, The Optimal Assignment Problem for a Countable State Space,
Proceedings of the International Conference on Tropical and Idempotent Mathematics, G.L. Litvinov and S.N. Sergeev Eds, volume 495 of Contemporary Mathematics,
pp. 39--60, AMS, 2009. Also arXiv:0812.4866.
M. Akian, S. Gaubert and A. Guterman, Linear independence over tropical semirings and beyond,
Proceedings of the International Conference on Tropical and Idempotent Mathematics, G.L. Litvinov and S.N. Sergeev Eds, volume 495 of Contemporary Mathematics,
pp. 1--38, AMS, 2009. Also arXiv:0812.3496.
P. Butkovic, R. A. Cuninghame-Green, S. Gaubert,
Reducible spectral theory with applications to the robustness of matrices in max-algebra, SIAM J. Matrix Anal. Appl., volume 31, number 3, pp. 1412--1431, 2009, doi:10.1137/080731232,
[pdf].
M. Akian, B. David, S. Gaubert.
Un théorème de représentation des solutions de viscosité
d'une équation d'Hamilton-Jacobi-Bellman ergodique dégénérée
sur le tore, C.R. Acad. Sci. Paris, Ser I 346 (2008) 1149-1154,
doi:10.1016/j.crma.2008.09.020
M. Akian, S. Gaubert, and A. Lakhoua
Convergence analysis of the max-plus finite element method for solving optimal control problems,
Proceedings of the 47th IEEE Conference on Decision and Control (CDC'08),
pp 927--934, Cancun, Mexico, doi:10.1109/CDC.2008.4739501
M. Akian and S. Gaubert and N. Ninove,
The T-PageRank: A Model of Self-Validating Effects of Web Surfing,
Proceedings of the Second Multidisciplinary International Symposium on
Positive Systems: Theory and Applications (POSTA'06), Grenoble, France,
August 30 - September 1 2006,
Lecture Notes in Control and Information Sciences, volume 341, 2006,
pp. 239--246, Springer.
doi:10.1007/11757344_31.
S. Gaubert and R. Katz,
Max-plus convex geometry,
in the Proceedings of the 9th International Conference on Relational
Methods in Computer Science and 4th International Workshop
on Applications of Kleene Algebra (RelMiCS/AKA 2006),
R. A. Schmidt (Ed), Lecture Notes in Comput. Sci.,
volume 4136, pp. 192-206, 2006,
Springer.
doi:10.1007/11828563_13.
M.Akian, R. Bapat, S. Gaubert,
Max-plus algebras,
Chapter 25 in the Handbook of Linear Algebra, L. Hogben, R. Brualdi,
A. Greenbaum, and R. Mathias (editors), Discrete Mathematics and Its Applications, Volume 39, Chapman and Hall, 2007, ISBN 1-58488-510-6, Second Edition,
ISBN 9781466507289, November 2013.
G. Cohen, S. Gaubert, and J.P. Quadrat
Projection and aggregation in maxplus algebra,
Current Trends in Nonlinear Systems and Control,
in Honor of Petar Kokotovic and Turi Nicosia,
Menini, Laura; Zaccarian, Luca; Abdallah, Chaouki T. (Eds.),
Birkhauser, January 2006, [pdf],.
G. Cohen, S. Gaubert, E. Mancinelli, J.P. Quadrat and E. Rofman,
On traffic light control,
Mathematicae Notae, Boletin del Instituto de Matematica "Beppo Levi",
Ano XLIII (2005), pp. 51-62, Universidad Nacional de Rosario Editora,
Rosario, Argentina. (Preliminary version available as
INRIA Report 4276,
Sep. 2001.)
M. Akian, S. Gaubert, B. Lemmens and R. Nussbaum.
Iteration of order preserving subhomogeneous maps on a cone,
Mathematical Proceedings of the Cambridge Philosophical Society,
volume 140, pages 157--176, 2006.
doi:doi:10.1017/S0305004105008832.
Also
arXiv:math.DS/0410084.
M. Akian, S. Gaubert and C. Walsh.
Discrete max-plus spectral theory
ESI Preprint 1485, arXiv:math.SP/0405225. Appears in Idempotent Mathematics and Mathematical Physics,
G.L. Litvinov and V.P. Maslov, Eds, vol. 377 of Contemporary Mathematics, pp. 53--77, AMS, 2005.
M. Akian, S. Gaubert and A. Lakhoua.
A max-plus finite element method for solving finite horizon deterministic optimal control problems,
INRIA RR-5163, arXiv:math.OC/0404184. Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS2004), Louvain, Belgique, Jul. 2004 (proceedings on cdrom, no page numbers).
M. Akian, S. Gaubert and V. Kolokoltsov.
Set coverings and invertibility of functional Galois connections
ESI Preprint 1447, arXiv:math.FA/0403441.
Appears in Idempotent Mathematics and Mathematical Physics,
G.L. Litvinov and V.P. Maslov, Eds, vol. 377 of Contemporary Mathematics, pp. 19--51, AMS, 2005.
M. Akian, R. Bapat and S. Gaubert.
Perturbation of eigenvalues of matrix pencils and optimal assignment problem
C. R. Acad. Sci. Paris, Série I, volume 339 (2004),
pages 103-108.
doi:doi:10.1016/j.crma.2004.05.001
Also arXiv:math.SP/0402438.
M. Akian, R. Bapat and S. Gaubert.
Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theoremarXiv:math.SP/0402090,
(preliminary version as INRIA RR-5104, Feb. 04).
S. Gaubert and R. Katz.
Reachability problems for products of matrices in semirings.
INRIA RR-4944, Sep. 03. International Journal of Algebra and Computation, Vol. 16, No. 3 (2006) 603-627, doi:doi:10.1142/S021819670600313XarXiv:math.OC/0310028
G. Cohen, S. Gaubert and J.P. Quadrat and I. Singer.
Max-plus convex sets and functions.
ESI preprint 1341, Jul. 2003.
arXiv:math.FA/0308166.
Appears in Idempotent Mathematics and Mathematical Physics,
G.L. Litvinov and V.P. Maslov, Eds, vol. 377 of Contemporary Mathematics, pp. 105--129, AMS, 2005.
G. Cohen, S. Gaubert and J.P. Quadrat.
Duality and Separation Theorems in Idempotent Semimodules.
Linear Algebra and Appl., Volume 379, pages 395--422, 2004.
doi:10.1016/j.laa.2003.08.010
Also arXiv:math.FA/0212294.
M. Akian, S. Gaubert and V. Kolokoltsov.
Invertibility of Functional Galois Connections.
C. R. Acad. Sci. Paris, Série I, Vol. 335 (2002), p. 883-888.
doi:10.1016/S1631-073X(02)02594-3[pdf],
[ps],
[ps.gz]
S. Gaubert and R. Katz.
Rational semimodules over the max-plus semiring and geometric approach of discrete event systems.
Kybernetika, volume 40 (2004), number 2, pages 153-180.
Czech Digital Mathematics Library #35586
Also arXiv:math.OC/0208014.
M. Akian and S. Gaubert.
Spectral theorem for convex monotone homogeneous maps, and ergodic control, INRIA-RR-4273, October 2001, arXiv:math.SP/0110108 Nonlinear Analysis, TMA.,
volume 52, number 2, pages 637--679, 2003. doi:10.1016/S0362-546X(02)00170-0
M. Akian and R.B. Bapat and S. Gaubert.
Generic asymptotics of eigenvalues using (min,+) algebra,
Proceedings of the Satellite Workshop on Max-Plus
Algebras, IFAC SSSC'01, Praha, Aug. 2001.
[pdf],
[ps],
[ps.gz]
M. Akian and S. Gaubert.
A spectral theorem for convex monotone homogeneous maps,
Proceedings of the Satellite Workshop on Max-Plus
Algebras, IFAC SSSC'01, Praha, Aug. 2001. Elsevier.
[ps], [ps.gz] This is a short announce of the result which
has been detailed in
arXiv:math.SP/0110108.
P. Butkovic and S. Gaubert,
Sign-non-singular matrices and matrices with unbalanced determinant in symmetrised semirings, Linear Algebra and Appl., 301, pp. 195-201, 1999.
doi:10.1016/S0024-3795(99)00201-3
Stéphane Gaubert, Jeremy Gunawardena,
A Non-Linear Hierarchy for Discrete Event Dynamical Systems,
Proceedings of WODES'98, Cagliari, Italia, pp. 249-254, Aug 1998.
[pdf],
[ps],
[ps.gz]
Jean Cochet-Terrasson, Guy Cohen, Stephane Gaubert, Michael Mc Gettrick,
Jean-Pierre Quadrat,
Numerical computation of spectral elements in max-plus algebra,
IFAC Conference on System Structure and Control, 1998,
Pergamon press,
[pdf],
[ps],
[ps.gz]
Albert Benveniste and Stéphane Gaubert and Claude Jard,
Monotone rational series and max-plus algebraic models
of real-time systems,
Proc. of the Fourth Workshop on Discrete Event Systems (WODES98),
IEE,
Cagliari, Italy,
1998. [pdf]
A. Benveniste and C. Jard and S. Gaubert,
Algebraic techniques for timed systems,
Proceedings of CONCUR'98
number 1466 in LNCS, Springer, 1998
(Nice, France, Septembre 1998).
doi:10.1007/BFb0055636[pdf]
S. Gaubert, J. Mairesse, Modeling and Analysis of Timed Petri Nets using Heaps of Pieces,
IEEE Trans. Aut. Control, 44(4):683--697, 1999.
doi:10.1109/9.754807[pdf],
[ps],[ps.gz]
An abridged version appeared in the Proceedings of the ECC97.
ECC version.psECC version.ps.gz
Task Resource Models and (max,+) Automata, S. Gaubert, J. Mairesse, 1995.
Appears in Idempotency, J. Gunawardena Ed.
Collection of the Isaac Newton Institute,
Cambridge University Press, 1998.
Abstract.html,
[ps], [ps.gz], [pdf]
Algebraic System Analysis of Timed Petri Nets,
G. Cohen, S. Gaubert and J. P. Quadrat, 1995.
Appears in Idempotency, J. Gunawardena Ed.
Collection of the Isaac Newton Institute,
Cambridge University Press, 1998.
Abstract.html,
[ps],
[ps.gz],
[pdf]
G. Cohen, S. Gaubert, J.P. Quadrat,
Timed Event Graphs with Multipliers and Homogeneous Min-Plus Systems,
IEEE-TAC, Vol 43, N. 9, Sep 1998.
doi:10.1109/9.718621[pdf], [ps], [ps.gz]
S. Gaubert and M. Plus, Methods and Applications of (max,+) Linear Algebra,
Proceedings of
the 14th Annual Symposium on Theoretical Aspects of Computer Science Lubeck, Germany February 27 - March 1, 1997 (STACS'97), pp 261-282,
LNCS 1200, Springer, 1997,
doi:10.1007/BFb0023465
A survey paper with emphasis on linear algebra.
Max-Plus working group (collective name),
Max-Plus-Times Linear Systems In: V.D. Blondel, E.D. Sontag, M. Vidyasagar, J.C. Willems (Eds.), Open Problems in Mathematical Systems and Control Theory, Communications and Control Engineering series, Springer Verlag, London, 1999.
J.P. Quadrat and the Max-Plus Working group (collective name),
Min-Plus Linearity and statistical mechanics,
Markov Processes and Related Fields, Vol. 3, N.
4, pp 565--587 (1997).
[pdf],
[ps], [ps.gz]
S. Gaubert, On the Burnside Problem for semigroups of matrices in the (max,+) algebra.
Semigroup Forum, Vol. 52 (1996), pp. 271--292.
doi:10.1007/BF02574104Abstract.html,
[pdf][ps] The SF published
version had a minor LaTeX numbering problem independent
of the author
(see the Corrigendum on the SF site). The version provided here is mathematically identical, but without this issue.
S. Gaubert and A. Giua, Petri Net Languages With Infinite Sets of Final Markings.
Feb. 1995. Proceedings of WODES' 96.
Edinburgh, Scotland, UK, 19-21 August, 1996. Abstract
G. Cohen and S. Gaubert and J.P. Quadrat,
Asymptotic Throughput of Continuous Timed Petri Nets
Proceedings of the 34th Conference on
Decision and Control,
New Orleans,
Dec,
1995.
doi:10.1109/CDC.1995.480646Abstract.html, [ps], [ps.gz], [pdf]
G. Cohen, S. Gaubert, J.P. Quadrat,
Kernels, images and projections in dioids.
Proceedings of the third international workshop on Discrete Event Systems
(WODES'96), IEE, Edinburgh, Scotland, UK, August 19-21, 1996.
Abstract[ps] (size 3MB !),
[ps.gz]
(1.4MB)
[pdf](0.7MB)
S. Gaubert, Performance Evaluation of (max,+) Automata,
IEEE Trans. on Automatic Control, 40(12),
pp. 2014--2025, Dec. 1995.
doi:10.1109/9.478227Abstract.html, [pdf], [ps]
An anouncement of these results appeared in the Proceedings of the ECC93,
Groningen, July 1993.
S. Gaubert,
Rational Series over Dioids and Discrete Event Systems,
Proc. of the 11th Conf. on Anal. and Opt. of Systems:
Discrete Event Systems,
number 199 in Lect. Notes. in Control and Inf. Sci, Springer, 1994
(June 1994, Sophia Antipolis).
doi:10.1007/BFb0033554Abstract.html,
[ps], [ps.gz], [pdf],
G. Cohen and S. Gaubert and J.P. Quadrat, From first to second-order theory of linear discrete event systems,
12th IFAC, Sydney,
Jul., 1993. Abstract.html.
M. Plus,
A linear system theory for systems subject to synchronization
and saturation constraints.
Proceedings of the first European Control Conference
Grenoble, July 1991. Abstract,[pdf][ps.gz].
Cohen, G.; Gaubert, S.; Nikoukhah, R.; Quadrat, J.P.,
Second order theory of min-linear systems
and its application to discrete event systems.
Proceedings of the 30th CDC,
Brighton, Dec. 1991.
Abstract.doi:10.1109/CDC.1991.261654[pdf]
S. Gaubert and C. Klimann,
Rational computation in dioid algebra and
its application to performance evaluation of Discrete
Event Systems,
In Algebraic computing in control,
G. Jacob and F. Lamnabhi-Lagarrigue Eds,
Lecture Notes in Control and Inf. Sci.
number 165, 1991,
Springer.
doi:10.1007/BFb0006942[pdf]
S. Gaubert, An algebraic method for optimizing resources in timed event graphs.
Proceedings of the 9th International Conference on Analysis
and Optimization of Systems, A.Bensoussan and J.L. Lions Eds,
Lecture Notes in Control and Information Sciences number 144,
Springer 1990. Abstract.html
M. Plus, L'algèbre (max,+) et sa symétrisation ou l'algèbre des
équilibres. Comptes Rendus à l'Académie des Sciences, Section Automatique, volume 311, number 4, pp 443--448, 1990. [pdf] (scanned file from Gallica).