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The characterization of maximal invariant sets of non-linear discrete-time control dynamical systems

Pages: 393 - 406, Issue special, November 2013

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Byungik Kahng - Department of Mathematics and Information Sciences, University of North Texas at Dallas, Dallas, TX 75241, United States (email)
Miguel Mendes - Departamento de Engenharia Civil, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias 4200 - 465 Porto, Portugal (email)

Abstract: The main topic of this paper is the controllability/reachability problems of the maximal invariant sets of non-linear discrete-time multiple-valued iterative dynamical systems. We prove that the controllability/reachability problems of the maximal full-invariant sets of classical control dynamical systems are equivalent to those of the maximal quasi-invariant sets of disturbed control dynamical systems, when modeled by the iterative dynamics of multiple-valued self-maps. Also, we prove that the afore-mentioned maximal full-invariant sets and maximal quasi-invariant sets are countably infinite step controllable under some appropriate conditions. We take an abstract set theoretical approach, so that our main theorems remain valid regardless of the topological structure of the space or the analytical structure of the dynamics.

Keywords:  Maximal invariance, controllability, orbit-chain.
Mathematics Subject Classification:  Primary: 93C05, 93C25, 93C55; Secondary: 37E99.

Received: September 2012;      Revised: March 2013;      Published: November 2013.

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