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Necessary optimality conditions for quasi-singular controls for systems with Caputo fractional derivatives

Yusubov Shakir Sh., Mahmudov Elimhan N.

Archives of Control Sciences

2023

Vol. 33, No. 3

463--496

In this paper, we consider an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation. First we get the linearized maximum principle. Further, the concept of a quasi-singular control is introduced and, on this basis, an analogue of the Legendre-Clebsch conditions is obtained. When the analogue of Legendre-Clebsch condition degenerates, a necessary high-order optimality condition is derived. An illustrative example is considered.