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

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.