American Institute of Mathematical Sciences

Advanced
2015, 2015(special): 723-732. doi: 10.3934/proc.2015.0723

On control synthesis for uncertain dynamical discrete-time systems through polyhedral techniques

Elena K. Kostousova 1,

1. 

N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16, S.Kovalevskaja street, Ekaterinburg, 620990, Russian Federation

Received  July 2014 Revised  January 2015 Published  November 2015

Problems of feedback terminal target control for linear discrete-time systems without and with uncertainties are considered. We continue the development of methods of control synthesis using polyhedral (parallelotope-valued) solvability tubes. The cases without uncertainties, with additive parallelotope-bounded uncertainties, and also with interval uncertainties in coefficients of the system are considered. Also the same systems under state constraints are considered. Nonlinear recurrent relations are presented for polyhedral solvability tubes for each of the mentioned cases. Two types of control strategies, which can be calculated on the base of the mentioned tubes, are proposed. Controls of the second type can be calculated by explicit formulas. Results of computer simulations are presented.
Keywords: parallelotopes, polyhedral estimates, parallelepipeds, control synthesis, Discrete-time systems, interval analysis., uncertain systems.
Mathematics Subject Classification: Primary: 93C41, 93C55, 93B52; Secondary: 93B40, 52B1.
Citation: Elena K. Kostousova. On control synthesis for uncertain dynamical discrete-time systems through polyhedral techniques. Conference Publications, 2015, 2015 (special) : 723-732. doi: 10.3934/proc.2015.0723
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show all references

References:
[1]

Dokl. Akad. Nauk, 434, no. 3 (2010), 319-323 [Russian], Transl. as Dokl. Math., 82 (2010), 831-834.  Google Scholar

[2]

in Modeling Techniques for Uncertain Systems (Sopron, 1992), (eds. A. B. Kurzhanski and V. M. Veliov), Progr. Systems Control Theory, vol. 18, Birkhäser, Boston (1994), 71-92.  Google Scholar

[3]

Nauka, Moscow, 1987 [Russian].  Google Scholar

[4]

IEEE Trans. Automat. Control., AC-24 (1979), 346-349.  Google Scholar

[5]

CRC Press, Boca Raton, 1994. Google Scholar

[6]

Zh. Vychisl. Mat. Mat. Fiz., 53, no.1 (2013), 47-57 [Russian], Transl. as Comput. Math. Math. Phys., 53, no.1 (2013), 34-43.  Google Scholar

[7]

Discrete Contin. Dyn. Syst. 2011, Dynamical systems, differential equations and applications, 8th AIMS Conference, Suppl. vol. I (2011), 410-419.  Google Scholar

[8]

Avtomat. i Telemekh., no. 3 (2012), 39-51 [Russian], Transl. as Autom. Remote Control, 73 (2012), 450-461.  Google Scholar

[9]

Optim. Methods Softw., 14 (2001), 267-310.  Google Scholar

[10]

Computational Technologies, 8 (2003), 55-74 [Russian; also available from: http://www.ict.nsc.ru/jct/search/article?l=eng]. Google Scholar

[11]

Algorithms and Software for Parallel Computations, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg, vol.9, (2006), 84-105 [Russian].  Google Scholar

[12]

Discrete Contin. Dyn. Syst. 2011, Dynamical systems, differential equations and applications, 8th AIMS Conference, Suppl. vol. II (2011), 864-873.  Google Scholar

[13]

AIP Conf. Proc., 1493 (2012), 579-586; doi: http://dx.doi.org/10.1063/1.4765545. Google Scholar

[14]

Nauka, Moscow, 1974 [Russian].  Google Scholar

[15]

Problemy Upravlen. Inform., no.1 (2010), 5-21 [Russian], Transl. as J. Automation and Inform. Sci., 42 (2010), 1-18.  Google Scholar

[16]

Mat. Sb. 191, no. 6 (2000), 69-100 [Russian], Transl. as Sb. Math., 191 (2000), 849-881.  Google Scholar

[17]

Dokl. Akad. Nauk SSSR, 311, no. 4 (1990), 788-793 [Russian], Transl. as Soviet Math. Doklady, 41 (1990), 300-305.  Google Scholar

[18]

Birkhäuser, Boston, 1997.  Google Scholar

[19]

Birkhäuser Basel, 2014.  Google Scholar

[20]

SIAM Journal of Optimization, 9 (1998), 112-147.  Google Scholar

[21]

Nauka, Moscow, 2002 [Russian]. Google Scholar

[22]

Cambridge Univ. Press, Cambridge, 1993.  Google Scholar

[23]

Izv. Ross. Akad. Nauk Tekhn. Kibernet., no. 3 (1994) 173-185 [Russian], Transl. as J. Comput. Systems Sci. Internat., 33, no.6 (1995), 127-139.  Google Scholar

[24]

Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg, 2005 [Russian].  Google Scholar

[25]

Izv. Akad. Nauk Teor. Sist. Upr., no.3 (2000), 70-77 [Russian].  Google Scholar

[26]

Systems Control Lett., 13, no.3 (1989), 263-269.  Google Scholar

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