Advances in Differential Equations and Control Processes

The Advances in Differential Equations and Control Processes is an esteemed international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research articles related to recent developments in both theory and applications of ordinary and partial differential equations, integral equations, and control theory. The journal highlights the interdisciplinary nature of these topics, with applications in physical, biological, environmental, and health sciences, mechanics, and engineering. It also considers survey articles that identify future avenues of advancement in the field.

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NECESSARY CONDITIONS FOR OPTIMALITY IN ONE NONSMOOTH OPTIMAL CONTROL PROBLEM FOR GOURSAT-DARBOUX SYSTEMS

Authors

  • Aysel T. Ramazanova

Keywords:

optimal control, necessary conditions, hyperbolic equations

DOI:

https://doi.org/10.17654/0974324324034

Abstract

We consider a nonsmooth optimal control problem described by a system of second-order hyperbolic equations with Goursat boundary conditions. A number of necessary optimality conditions are proved in terms of directional derivatives.

Received: October 11, 2024
Accepted: October 21, 2024

References

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R. Gabasov and F. M. Kirillova, Book: The Maximum Principle in the Theory of Optimal Control by M. Liebrock, Vol. 22, 2011, 272 pp.

V. I. Sumin, Functional Volterra equations in the theory of optimal control with distributed systems, UNN Publishing House, Nizhny-Novgorod, 1992, 110 pp.

M. B. Suryanarayana, Necessary conditions for optimization problems with hyperbolic partial differential equations, SIAM Journal on Control 11 (1973), 130-147.

S. S. Akhiev and T. K. Akhmedov, On the integral representation of solutions of some systems of differential equations, Izvestia, An Azerbaijan. SSR. Ser. Phys.- Techn. and Math. Sci. 11 (1973), 116-120.

V. V. Alsevich, Necessary optimality conditions for minimax optimal control problems, Differential Equations 8 (1976), 1384-1391.

D. A. Juraev, Theory of ill-posed problems for solving applied mathematics equations, Center for Computer Science, Mathematics, and Engineering Physics Journal 1 (2023), 1-10.

A. Telman Ramazanova, Necessary conditions for the existence of a saddle point in one optimal control problem for systems of hyperbolic equations, European Journal of Pure and Applied Mathematics 14(4) (2021), 1402-1414.

Kyazim K. Hasanov and Leila K. Hasanova, Necessary conditions of optimality in Goursat-Darboux problem with generalized controls, Journal of Automation and Information Sciences 33(5-8) (2001), 9.

An Li and Jane J. Ye, Necessary optimality conditions for optimal control problems with non smooth mixed state and control constraints, Set-Valued and Variational Analysis 24 (2016), 449-470.

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Published

2024-11-08

Issue

Vol. 31 No. 4 (2024)

Section

Articles

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How to Cite

NECESSARY CONDITIONS FOR OPTIMALITY IN ONE NONSMOOTH OPTIMAL CONTROL PROBLEM FOR GOURSAT-DARBOUX SYSTEMS. (2024). Advances in Differential Equations and Control Processes, 31(4), 673-681. https://doi.org/10.17654/0974324324034

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