The invariant set theory of multiple valued iterative dynamical systems

Authors:
Byungik Kahng
Affiliations:
University of Minnesota, Morris, Division of Science and Mathematics, Morris
Venue:
ICOSSSE'08 Proceedings of the 7th WSEAS international conference on System science and simulation in engineering
Year:
2008

Citing 4
Cited 0

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Brief paper: Feedback and invariance under uncertainty via set-iterates

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Survey paper: Set invariance in control

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Survey Constrained model predictive control: Stability and optimality

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Abstract

Invariant set theory is an important tool in the control theory. It has rich history that goes back over a century, yet it is still an active research topic both in pure mathematics and theoretical engineering. It is easy to reduce a traditional discrete-time control dynamical system to an iterative dynamics of one endomorphism in the phase space. It is not easy to do the same in the presence of the disturbance. The purpose of this paper is to show that we can overcome this difficulty using the dynamics of multiple valued maps. As an application, we study the reachability problem of the maximal positively invariant set, using the multiple valued dynamics.