Optimal control of fractional neutral stochastic differential equations with deviated argument governed by Poisson jumps and infinite delay

Abstract

Summary In this work, the optimal control for a class of fractional neutral stochastic differential equations with deviated arguments driven by infinite delay and Poisson jumps is studied in Hilbert space involving the Caputo fractional derivative. The sufficient conditions for the existence of mild solution results are formulated and proved by the virtue of fractional calculus, characteristic solution operator, fixed‐point theorem, and stochastic analysis techniques. Furthermore, the existence of optimal control of the proposed problem is presented by using Balder's theorem. Finally, the obtained theoretical results are applied to the fractional stochastic partial differential equations and a stochastic river pollution model.

Existence, Uniqueness, and Averaging Principle of Fractional Neutral Stochastic Differential Equations in the Lp Space with the Framework of the Ψ-Caputo Derivative

“…They provide a more accurate representation of dynamical systems with feedback mechanisms, allowing for better control strategies in various engineering applications. For more details about applications of FrNSDEs, see [27][28][29][30]. These applications demonstrate the versatility of FrNSDEs in modeling diverse systems with memory effects and stochastic dynamics, offering insights into complex phenomena across various disciplines.…”

Fractal variational principle for an optimal control problem

“…The constant λ≥0 can be viewed as a measure of the energy costs needed to implement the control, and it also serves as a regularization parameter. 33 The constraint of equation (4) of the multiple-level optimization can also be written as a differential equation…”

“…30 Finally, the fractal oscillators are also a hot topic in mathematics and engineering. 31,32 The traditional optimization theory [33][34][35][36] is used to couple, for the first time ever, the two-scale fractal calculus in this paper, improving its applicability in engineering. For example, we can use a flexible temperature sensor immersed in a cloth to guarantee an optimal temperature during the working time, yet the air conditioning would maintain the maximum energy efficiency.…”

Robustness of Hopfield Neural Networks Described by Differential Algebraic Systems of Index-1 under the Conditions of Deviation Argument and Stochastic Disturbance

“…In [11], the control scheme of a sequence of hybrid systems was improved by using sampling data control and pulse control. In [12], the optimal control problem of a system is solved. A series of notable issues have been comprehensively analysed, including out-synchronization and matrix measure approaches for stability and synchronization [13][14][15].…”