On polyhedral estimates for trajectory tubes of dynamical discrete-time systems with multiplicative uncertainty

Pages: 864 - 873, Volume 2011, Issue Special, September 2011      doi:10.3934/proc.2011.2011.864

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Elena K. Kostousova - Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16, S.Kovalevskaja Street, Ekaterinburg GSP-384, 620219, Russian Federation (email)

Abstract: The approach for constructing external and internal polyhedral (parallelepiped-valued) estimates of reachable sets and trajectory tubes for the discrete-time systems with a multiplicative uncertainty (for linear systems with the uncertainty in initial states, additive controls and system matrices) is presented. The techniques for set-valued operations using parallelepipeds and parallelotopes as basic sets are described. The solution to an auxiliary problem of finding an internal estimate for the set which is obtained by multiplying an interval matrix on a parallelotope is presented. Recurrence relations for evolution of estimates of reachable sets (cross-sections of trajectory tubes) are described. All proposed estimates can be calculated by explicit formulas. The results of numerical simulations are presented.

Keywords:  Dynamical systems, discrete-time systems, reachable sets, set-valued state estimation, multiplicative uncertainty, polyhedral estimates, parallelepipeds, parallelotopes.
Mathematics Subject Classification:  Primary: 93B03, 93C10, 93C55, 93C41; Secondary: 52B12

Received: July 2010;      Revised: April 2011;      Available Online: October 2011.