An accurate and straightforward method for solving optimal control problems using the second-order finite difference formula

Document Type : Original Paper

Authors

1 Department of Electrical Engineering, University of Bojnord, Bojnord, Iran

2 Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran

3 Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran

Abstract

In this paper, a simple and highly accurate approximate method for solving optimal control problems (OCPs) is presented. In this method, initially, by using the necessary optimality conditions based on the Pontryagin's maximum principle, the given OCP is transformed into a two-point boundary value problem (BVP). Then, by applying a second order finite difference formula, the resulting BVP is discretized, and a system of algebraic equations is formulated. Convergence analysis of the proposed method is also discussed, and matrix formulations are provided for ease of implementation. The numerical results obtained in this study are compared with some other methods, demonstrating the high accuracy, speed, and efficiency of the proposed method for solving both linear and nonlinear OCPs.

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References

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Journal of Advanced Mathematical Modeling
Volume 13, Issue 4 - Serial Number 32
February 2024
Pages 545-555

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History

  • Receive Date: 19 April 2023
  • Revise Date: 14 February 2024
  • Accept Date: 01 March 2024

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