On a generalized boundary value problem for a feedback control system with infinite delay

M. S. Afanasova   ; V. V. Obukhovskii   ; G. G. Petrosyan

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 2, pp. 167-185

Résumé

We consider a non-local boundary value problem for a feedback control system described by a semilinear functional-differential inclusion of fractional order with infinite delay in a separable Banach space. The general principle of existence of solutions to the problem in terms of the difference from zero of the topological degree of the corresponding vector field is given. We prove a concrete example (Theorem 6) of the implementation of this general principle. The existence of an optimal solution to the posed problem is proved, which minimizes the given lower semicontinuous quality functional.

Détail

Keywords: feedback control system, fractional differential inclusion, infinite delay, measure of noncompactness, condensing operator, fixed point, topological degree.
Mots-clés : optimal solution

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