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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.