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

• Type: Article in International Scientific Journal
• Date: 2013

Authors

Miguel Mendes (Author) FEUP; Byungik Kahng (Author) Other

Journal

Title: Discrete and Continuous Dynamical Systems

Serial No. supplement 2013

Pages: 393-406

ISSN: 1078-0947

Publisher: American Institute of Mathematical Sciences

Indexing

Scopus

Other information

Abstract (EN): The main topic of this paper is the controllability/reachability problems of the maximal invariant sets of non-linear discrete-time multiplevalued 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14