Necessary Optimality Conditions for Singular Controls of Caputo Fractional Systems with Delay in Control
Qualitative Theory of Dynamical Systems, vol.24, no.2, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 24 Issue: 2
- Publication Date: 2025
- Doi Number: 10.1007/s12346-025-01225-x
- Journal Name: Qualitative Theory of Dynamical Systems
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Keywords: Caputo fractional, Delay, Increment method, Necessary conditions, Singular controls
- Open Archive Collection: Article
- Azerbaijan State University of Economics (UNEC) Affiliated: No
Abstract
In this paper, we consider the optimal control of nonlinear systems of fractional-order with control delay, where the fractional derivatives are expressed in the Caputo sense. For this problem, we first obtained the necessary first-order optimality condition in the form of the Pontryagin maximum principle. For a control that is singular in the sense of the Pontryagin maximum principle, a higher-order necessary optimality condition is obtained. Further, in one particular case, a multipoint necessary second-order optimality condition is obtained. The effectiveness of the results obtained is illustrated by specific examples.