Metaheuristic-Based Algorithms for Optimizing Fractional-Order Controllers—A Recent, Systematic, and Comprehensive Review

Ahmed M. Nassef, Mohammad Ali Abdelkareem, Hussein M. Maghrabie, Ahmad Baroutaji

Research output: Contribution to journalReview articlepeer-review


Metaheuristic optimization algorithms (MHA) play a significant role in obtaining the best (optimal) values of the system’s parameters to improve its performance. This role is significantly apparent when dealing with systems where the classical analytical methods fail. Fractional-order (FO) systems have not yet shown an easy procedure to deal with the determination of their optimal parameters through traditional methods. In this paper, a recent, systematic. And comprehensive review is presented to highlight the role of MHA in obtaining the best set of gains and orders for FO controllers. The systematic review starts by exploring the most relevant publications related to the MHA and the FO controllers. The study is focused on the most popular controllers such as the FO-PI, FO-PID, FO Type-1 fuzzy-PID, and FO Type-2 fuzzy-PID. The time domain is restricted in the articles published through the last decade (2014:2023) in the most reputed databases such as Scopus, Web of Science, Science Direct, and Google Scholar. The identified number of papers, from the entire databases, has reached 850 articles. A Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology was applied to the initial set of articles to be screened and filtered to end up with a final list that contains 82 articles. Then, a thorough and comprehensive study was applied to the final list. The results showed that Particle Swarm Optimization (PSO) is the most attractive optimizer to the researchers to be used in the optimal parameters identification of the FO controllers as it attains about 25% of the published papers. In addition, the papers that used PSO as an optimizer have gained a high citation number despite the fact that the Chaotic Atom Search Optimization (ChASO) is the highest one, but it is used only once. Furthermore, the Integral of the Time-Weighted Absolute Error (ITAE) is the best nominated cost function. Based on our comprehensive literature review, this appears to be the first review paper that systematically and comprehensively addresses the optimization of the parameters of the fractional-order PI, PID, Type-1, and Type-2 fuzzy controllers with the use of MHAs. Therefore, the work in this paper can be used as a guide for researchers who are interested in working in this field.
Original languageEnglish
Article number553
Number of pages30
JournalFractal and Fractional
Issue number7
Early online date17 Jul 2023
Publication statusPublished - Jul 2023

Bibliographical note

Copyright © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (

Funding: This study was sponsored by the Prince Sattam bin Abdulaziz University via project number 2023/RV/016.


  • metaheuristics
  • fractional-order
  • optimization
  • PID controller
  • fuzzy logic


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