A Sub-Ordinary Approach to Achieve Near-Exact Solutions for a Class of Optimal Control Problems

Hashemi Borzabadi, Akbar; Gholami Baladezaei, Mohammad; Ghachpazan, Morteza

doi:10.30473/coam.2024.70834.1254

Document Type : Research Article

Authors

¹ Department of Applied Mathematics‎, ‎University of Science and Technology of Mazandaran‎, ‎Behshahr‎, ‎Iran.

² Department of Mathematics‎, ‎Damghan Branch‎, ‎Islamic Azad‎ ‎University‎, ‎Damghan‎, ‎Iran.

³ Department of Applied Mathematics‎, ‎School of Mathematical‎ ‎Sciences‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran‎.

10.30473/coam.2024.70834.1254

Abstract

This paper explores the advantages of Sub-ODE strategy in deriving near-exact‎ ‎solutions for a class of linear and nonlinear optimal control‎ ‎problems (OCPs) that can be transformed into nonlinear‎ ‎partial differential equations (PDEs). Recognizing that converting an OCP into differential‎ ‎equations typically increases the complexity by adding constraints‎, ‎we adopt the‎ ‎Sub-ODE method‎, ‎as a direct method‎, thereby negating the need for such transformations to extract near exact solutions‎. A key advantage of this method is its ability to produce control and state functions that closely resemble the explicit forms of optimal control and state functions. ‎ We present results that demonstrate the efficacy of this method through several numerical examples, comparing its performance to various other approaches, thereby illustrating its capability to achieve near-exact solutions.

Keywords

Main Subjects

Optimal Control

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A Sub-Ordinary Approach to Achieve Near-Exact Solutions for a Class of Optimal Control Problems

References

References

Articles in Press, Accepted Manuscript Available Online from 02 October 2024

Articles in Press, Accepted Manuscript
Available Online from 02 October 2024