Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

Pontryagin maximum principle for solving interval linear quadratic optimal control problems

Document Type : Original Article

Authors
Sima Salarzaei 1
Somayeh Rezaei-Zadeh 1
Mehdi Allahdadi 2
Samaneh Soradi-Zeid 3
1 Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
2 Mathematics Faculty, zahedan. Iran
3 Faculty of Industry and Mining Khash. University of Sistan and Baluchestan, Zahadean, Iran
10.22034/jfsa.2025.538880.1280
Abstract
In this paper, the solution of optimal control problems with a quadratic objective function and a linear dynamic system with interval coefficients is investigated. By studying the previous approaches to solving these problems, we will show that the results presented in these methods, despite solving deterministic sub models of the interval optimal control problem, ultimately lead to inaccurate approximations of the optimal solution. Therefore, considering the inherent complexity of dynamic systems and the problems caused by uncertainty, there is a need to develop new algorithms to achieve efficient criteria. The main goal of this paper is to present an efficient approach to solving this class of problems. Therefore, by modifying the existing algorithms, we make the resulting interval problem deterministic by transforming the Hamiltonian function into two upper and lower bound functions and obtain the solution to the problem by applying the Pontryagin conditions. This paper attempts to improve the accuracy and efficiency of previous methods in solving optimal control problems. MATLAB software has been used to obtain numerical results. Additionally, the results are reported in a base form so that they can be properly validated against results previously presented for these problems.
Keywords
Pontryagin extremum principle
Interval uncertainty
Optimal control problem
Interval optimal control

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Fuzzy Systems and its Applications
Volume 8, Issue 2 - Serial Number 17
Open Access Statement
December 2025
Pages 1-20

  • Receive Date 04 August 2025
  • Revise Date 19 October 2025
  • Accept Date 27 October 2025