Optimality conditions of singular controls for systems with Caputo fractional derivatives

Yusubov, Shakir Sh.; Mahmudov, Elimhan N.

doi:10.3934/jimo.2021182

Cited by 6 publications

(2 citation statements)

References 32 publications

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“…Although there are many articles on the maximum principle of stochastic and deterministic systems, there still remain many other interesting open problems concerning their fractional analogues, which can be extended by methods analogous to those used for fractional derivations of Caputo and Riemann-Liouville type. To this end, one can consider the method given in [30] to study the optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation.…”

Section: Discussionmentioning

confidence: 99%

Stochastic maximum principle for discrete time mean-field optimal control problems

Ahmadova

Mahmudov

2023

Preprint

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In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new version of the maximum principle for discrete-time mean-field type stochastic optimal control problems. Moreover, the cost functional is also of the mean-field type. This maximum principle differs from the classical principle one since we introduce new discrete-time mean-field backward (matrix) stochastic equations. Based on the discrete-time mean-field backward stochastic equations where the adjoint equations turn out to be discrete backward SDEs with mean field, we obtain necessary first-order and sufficient optimality conditions for the stochastic discrete mean-field optimal control problem. To verify, we apply the result to production and consumption choice optimization problem.

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Section: Discussionmentioning

confidence: 99%

Stochastic maximum principle for discrete time mean-field optimal control problems

Ahmadova

Mahmudov

2023

Preprint

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“…Although there are many articles on the maximum principle of stochastic and deterministic systems, there still remain many other interesting open problems concerning their fractional analogues, which can be extended by methods analogous to those used for fractional derivations of Caputo and Riemann‐Liouville type. To this end, one can consider the method given in Reference 33 to study the optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation.…”

Section: Discussionmentioning

confidence: 99%

Stochastic maximum principle for discrete time mean‐field optimal control problems

Ahmadova

Mahmudov

2023

Optim Control Appl Methods

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This article studies optimal control of a discrete‐time stochastic differential equation of mean‐field type with coefficients dependent on function of the law and state of the process. A new version of the maximum principle for discrete‐time mean‐field type stochastic optimal control problems is established, using new discrete‐time mean‐field backward stochastic equations. The cost functional is also of mean‐field type. The study derives necessary first‐order and sufficient optimality conditions using adjoint equations that take the form of discrete‐time backward stochastic differential equations with a mean‐field component. An optimization problem for production and consumption choice is used as an example.

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Finite time stability analysis for fractional stochastic neutral delay differential equations

Asadzade,

Mahmudov

2024

J. Appl. Math. Comput.

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In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique solution that satisfies given initial conditions. Furthermore, we extend our research to investigate the finite-time stability of the system by examining trajectory behavior over a given period. We employ advanced mathematical approaches to systematically prove finite-time stability, providing insights on convergence and stability within the stated interval. Using illustrative examples, we strengthen this all-encompassing examination into the complicated dynamics and stability features of fractionally ordered stochastic systems with time delays. The implications of our results extend to various fields, such as control theory, engineering, and financial mathematics, where understanding the stability of complex systems is crucial.

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Optimality conditions of singular controls for systems with Caputo fractional derivatives

Cited by 6 publications

References 32 publications

Stochastic maximum principle for discrete time mean-field optimal control problems

Stochastic maximum principle for discrete time mean-field optimal control problems

Stochastic maximum principle for discrete time mean‐field optimal control problems

Finite time stability analysis for fractional stochastic neutral delay differential equations

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