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

Elena K.  Kostousova

doi:10.3934/proc.2015.0723

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2015, Volume 2015: 723-732. Doi: 10.3934/proc.2015.0723 open access

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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

Received: July 2014

Revised: January 2015

Published: October 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 93C41, 93C55, 93B52; Secondary: 93B40, 52B12.

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