Optimal controls for second‐order stochastic differential equations driven by mixed‐fractional Brownian motion with impulses

Abstract

We study optimal control problems for a class of second‐order stochastic differential equation driven by mixed‐fractional Brownian motion with non‐instantaneous impulses. By using stochastic analysis theory, strongly continuous cosine family, and a fixed point approach, we establish the existence of mild solutions for the stochastic system. Moreover, the optimal control results are derived without uniqueness of mild solutions of the stochastic system. Finally, the main results are validated with the aid of an example.

Optimal control for fractional higher order damped stochastic impulsive systems

“…Remark The problems of solvability and optimal control of with impulse and without impulse fractional SDEs have been studied by many authors 25‐31 in infinite dimensional space. Till now, no literature is available in the finite dimensional space for dealing solvability and optimal control of fractional SDEs with impulsive effects.…”

Analysis and Optimal Control of φ-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions

“…The fractional OCP refers to optimize the cost functional subject to dynamical constraints on the control parameter and state variables that having fractional models. For more recent works on OCP, see [25][26][27][28][29][30] and the references therein. Harrat et al [31] investigated the existence of optimal controls for Hilfer fractional impulsive evolution inclusions with Clarke subdifferential.…”

Time Optimal Control of System Governed by a Fractional Stochastic Partial Differential Inclusion with Clarke Subdifferential

“…The optimal control theory has a considerable development, and one can find applications in many domains (see [9][10][11]13,33]). The time optimal control is an important topic in the theory of optimal controls and plays a vital role in control systems.…”