On solvability and optimal controls for impulsive stochastic integrodifferential varying-coefficient model

Abstract

This article concentrates in analyzing optimal controls for stochastic integrodifferential equation (SIDE) in Hilbert space. Necessary parameters are imposed to demonstrate the system that follows a unique variation of parameter formula using Leray Schauder Alternative. Subsequently, the existence of optimal control is investigated for the considered Lagrange control problem. The theoretical example with the mechanical example of ethanol fuelled engine are discussed to validate the results obtained.

KEYWORDS:

• Optimal control
• impulsive stochastic system
• time varying-coefficient model
• the Leray Schauder alternative

2010 AMS SUBJECT CLASSIFICATIONS:

• 35R10
• 60G22
• 60H20
• 93B05

Acknowledgments

The authors would like to thank the referees and the editor for their careful comments and valuable suggestions to improve this manuscript. All authors contributed equally in this research work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Ethical statement

No human and/or animal study is involved in this research, so this is not applicable.

Data availability statement

Authors have not used any scientific data to be determined for this research.