On a Random Topological Characteristic for Inclusions with Nonlinear Fredholm Operators: Application to Some Classes of Feedback Control Systems

Authors

  • Valeri Obukhovskii Voronezh State Pedagogical University, Voronezh, Russia
  • Sergey Kornev Voronezh State Pedagogical University, Voronezh, Russia
  • Ekaterina Getmanova Voronezh State Pedagogical University, Voronezh, Russia

DOI:

https://doi.org/10.25728/assa.2023.23.3.1390

Keywords:

feedback control system, random differential inclusion, random coincidence index, random coincidence point, nonlinear Fredholm operator, random multivalued map

Abstract

We define and study an oriented random coincidence index for a pair consisting of a nonlinear zero index Fredholm operator $f$ and a nonconvex - valued random multivalued map $G$ which is fundamentally restrictible with respect to $f.$ It is shown how this characteristic can be used for the justification of the existence of random coincidence points. We present an application of developed results to the existence of a random solution
for a control system whose dynamics is governed by an implicit integro-differential equation and the feedback is realized by a random differential inclusion.

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Published

2023-10-12

How to Cite

Obukhovskii, V., Kornev, S., & Getmanova, E. (2023). On a Random Topological Characteristic for Inclusions with Nonlinear Fredholm Operators: Application to Some Classes of Feedback Control Systems. Advances in Systems Science and Applications, 23(3), 48–65. https://doi.org/10.25728/assa.2023.23.3.1390

Issue

Vol. 23 No. 3 (2023): Advances in Systems Science and Applications

Section

Articles