SCIENTIA SINICA Informationis, Volume 46 , Issue 11 : 1633-1647(2016) https://doi.org/10.1360/N112016-00139

Timing optimal control and reliability of uncertain data transmission systems with interval parameters

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  • ReceivedAug 12, 2016
  • AcceptedOct 14, 2016
  • PublishedNov 10, 2016


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[1] Roddy D. {Satellite Communications}. New Jersey: Prentice Hall, 1989. Google Scholar

[2] Collinson R P G. {Introduction to Avionics Systems}. New York: Springer Science+Business Media, 2011. Google Scholar

[3] Dumas M B. {Principles of Computer Networks and Communications}. New Jersey: Prentice Hall, 2008. Google Scholar

[4] Cohen G, Dunois D, Quadrat J P, et al. A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing. newblock IEEE Trans Autom Contr, 1985, 30: 210-220 CrossRef Google Scholar

[5] Olsder G J. Applications of the theory of stochastic discrete-event systems to array processors and scheduling in public transportation. In: {Proceedings of the 28th IEEE Conference on Decision and Control}, Tampa, 1989. 2012-2017. Google Scholar

[6] Li Q, Zhang X, Xiong H. An optimization for packet delivery in integrated avionics systems. In: {Proceedings of the 23rd Digital Avionics Systems Conference}, Salt Lake City, 2004. Google Scholar

[7] Goverde R M P. Railway timetable stability analysis using max-plus system theory. {Transport Res B-Meth}, 2007, {41}: 179-201. Google Scholar

[8] Olsder G J, Roos C. Cramer and {C}ayley-{H}amilton in the max algebra. {Linear Algebra Appl}, 1988, 101: 87-108. Google Scholar

[9] D$\text{e\ }$Schutter B, De Moor B. A note on the characteristic equation in the max-plus algebra. newblock Linear Algebra Appl, 1997, 261: 237-250 CrossRef Google Scholar

[10] Chen W, Qi X, Deng S. The eigen-problem and period analysis of the discrete event system. {Syst Sci Math Sci}, 1990, 3: 243-260. Google Scholar

[11] Gaubert S. {Th$\acute{\text{e}}$orie des Syst$\grave{\text{e}}$mes Lin$\acute{\text{e}}$aires dans les Dioides}. Dissertation for Ph.D. Degree. Paris: L'Ecole Nationale Sup$\acute{\text{e}}$rieure des Mines de Paris, 1992. Google Scholar

[12] Gaubert S, Gunawardena J. The duality theorem for min-max functions. {Comptes Rendus de l'Acad$\acute{\text{e}}$mie des Sciences, Series I: Mathematics}, 1998, 326: 43-48. Google Scholar

[13] Zhao Q. A remark on inseparability of min-max systems. newblock IEEE Trans Autom Contr, 2004, 49: 967-970 CrossRef Google Scholar

[14] Butkovi$\check{c}$ P, MacCaig M. On integer eigenvectors and subeigenvectors in the max-plus algebra. newblock Linear Algebra Appl, 2013, 438: 3408-3424 CrossRef Google Scholar

[15] D$\text{e\ }$Schutter B, De Moor B. The {QR} decomposition and the singular value decomposition in the symmetrized max-plus algebra. newblock SIAM J Matrix Anal Appl, 1998, 19: 378-406 CrossRef Google Scholar

[16] Chen W, Qi X. Period assignment of discrete event dynamic systems. {Sci China Ser A}, 1993, 13: 1-7. Google Scholar

[17] Cohen G, Dubois D, Quadrat J P, et al. Linear system theory for discrete event systems. In: {Proceedings of the 23rd IEEE Conference on Decision and Control}, Las Vegas, 1984. 539-544. Google Scholar

[18] Wang L, Zheng D. On the reachability of linear discrete event dynamic systems. {Appl Math A J Chinese Univ}, 1990, 5: 292-301. Google Scholar

[19] Tao Y, Liu G-P, Mu X. Max-plus matrix method and cycle time assignability and feedback stabilizability for min-max-plus systems. {Math Contr Signals Syst}, 2013, {25}: 197-229. Google Scholar

[20] Adzkiya D, De Schutter B, Abate A. Computational techniques for reachability analysis of max-plus-linear systems. {Automatica}, 2015, {53}: 293-302. Google Scholar

[21] D$\text{e\ }$Schutter B, van den Boom T J J. Model predictive control for max-plus-linear discrete event systems. {Automatica}, 2001, {37}: 1049-1056. Google Scholar

[22] van den Boom T J J, De Schutter B. Properties of {MPC} for max-plus-linear systems. {Eur J Contr}, 2002, {8}: 453-462. Google Scholar

[23] Moore R E. {Methods and Applications of Interval Analysis}. Philadelphia: Society for Industrial and Applied Mathematics, 1979. Google Scholar

[24] Lhommeau M, Hardouin L, Cottenceau B, et al. Interval analysis and dioid: application to robust controller design for timed event graphs. {Automatica}, 2004, {40}: 1923-1930. Google Scholar

[25] Aubry C, Desmare R, Jaulin L. Loop detection of mobile robots using interval analysis. {Automatica}, 2013, {49}: 463-470. Google Scholar

[26] Zhang H, Tao Y, Zhang Z. Strong solvalibility of interval max-plus systems and applications to optimal control. {Syst Contr Lett}, 2016, {96}: 88-94. Google Scholar

[27] Cechl$\acute{\text{a}}$rov$\acute{\text{a}}$ K, Cuninghame-Green R A. Interval systems of max-separable linear equations. {Linear Algebra Appl}, 2002, {340}: 215-224. Google Scholar

[28] My$\check{\text{s}}$kov$\acute{\text{a}}$ H. Interval systems of max-separable linear equations. {Linear Algebra Appl}, 2005, {423}: 263-272. Google Scholar

[29] My$\check{\text{s}}$kov$\acute{\text{a}}$ H. Interval max-plus systems of linear equations. {Linear Algebra Appl}, 2012, {437}: 1992-2000. Google Scholar

[30] {Chakraborty S, Yun K Y, Dill D L. Timing analysis of asynchronous systems using time separation of events. {IEEE Trans Comput Aided Design Integr Circ Syst}, 1999, {18}: 1061-1076}. Google Scholar

[31] {Zhao Q, Mao J, Tao Y. Time separations of cyclic event rule systems with min-max timing constraints. {Theor Comput Sci}, 2008, {407}: 496-510}. Google Scholar

[32] Cuninghame-Green R A. {Minimax Algebra}. Berlin: Springer-Verlag, 1979. Google Scholar

[33] Baccelli F, Cohen G, Olsder G J, et al. {Synchronization and Linearity}. New York: John Wiley and Sons, 1992. Google Scholar

[34] Heidergott B, Olsder G J, van der Woude J. {Max-Plus at Work: Modeling and Analysis of Synchronized Systems}. New Jersey: Princeton University Press, 2006. Google Scholar

[35] Zimmermann K. {Extrem$\acute{\text{a}}$lni Algebra}. Praha: Ekonomicko-matematick$\acute{\text{a}}$ laborato$\check{\text{r}}$ Ekonomick$\acute{\text{e}}$ho $\acute{\text{u}}$stavu $\check{\text{C}}$SAV, 1976. Google Scholar

[36] Butkovi$\check{\rm c}$ P. {Max-Linear Systems: Theory and Algorithms}. Berlin: Springer-Verlag, 2010. Google Scholar

[37] Alefeld G, Herzberger J. {Introduction to Interval Computations}. New York: Academic Press, 1983. Google Scholar

[38] Alefeld G, Mayer G. Interval analysis: theory and applications. {J Comput Appl Math}, 2000, {121}: 421-464. Google Scholar

[39] Litvinov G L, Sobolevski$\breve{{\i}}$ A N. Idempotent interval analysis and optimization problems. {Reliable Comput}, 2001, {7}: 353-377. Google Scholar

[40] Cechl$\acute{\text{a}}$rov$\acute{\text{a}}$ K. Solutions of interval linear systems in max-plus algebra. In: Proceedings of the Symposium on Operations Research, Preddvor, 2001. 321-326. Google Scholar