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Fractal Fract
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Fractional Control Systems and Estimation: Control, State Observers and Parameter...
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Fractional Control Systems and Estimation: Control, State Observers and Parameter Estimation

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (15 December 2025) | Viewed by 6195

Special Issue Editors

Prof. Dr. Manuel A. Duarte-Mermoud

E-Mail Website
Guest Editor
Facultad de Ingeniería y Arquitectura, Universidad Central de Chile, Av.Santa Isabel 1186, Santiago 8330601, Chile
Interests: robust adaptive control (linear and nonlinear, fractional and integer order); system identification and parameter estimation; intelligent control and applications; adaptive systems and artificial intelligence
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Gustavo Ceballos-Benavides

E-Mail Website
Guest Editor
Facultad de Ingeniería y Arquitectura, Universidad Central de Chile, Av. Santa Isabel 1186, Santiago 8330601, Chile
Interests: fractional order adaptive control; robust control; optimal control; extended Kalman filter and signal processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In the past, results related to fractional order operators have been reported both in theory and application, covering different fields such as modeling, identification, estimation, observer design, control, and signal processing, among others. The interest in using fractional order tools has increased rapidly over the last few decades, with solid results being obtained for the study of fractional order systems and signals for transient behavior, stability, convergence, and boundedness viewpoints, allowing for a comparison of these techniques with those based on integer order derivative and integral operators, expanding the horizons of these topics.

The present Special Issue is devoted to new theories and applications, making use of fractional order operators and comparisons with their integer order counterparts. The topics of interest include, but are not limited to, the following areas:

  • Fractional order control (adaptive and non-adaptive) theory and practice;
  • Fractional systems analysis and design;
  • Fractional order observers and estimators;
  • Fractional parameter estimation;
  • Robust fractional order control;
  • FO PID controllers;
  • Fractional order sliding mode control and applications;
  • Stability of fractional order differential equations and systems;
  • Back-stepping fractional order control (adaptive and non-adaptive systems);
  • Fractional differential or difference equations;
  • Mathematical and numerical methods of fractional order control systems;
  • Theory and applications of fractional order identification and control.

Prof. Dr. Manuel A. Duarte-Mermoud
Prof. Dr. Gustavo Ceballos-Benavides
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • adaptive identification and control
  • robust control
  • PID control
  • parameter estimation
  • state observers
  • Liouville–Caputo
  • Riemann–Liouville
  • Grunwald–Letnikov
  • adaptive systems and artificial intelligence

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Related Special Issue

Published Papers (5 papers)

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Research

19 pages, 3119 KB  
Article
Earthquake-Resilient Structural Control Using PSO-Based Fractional Order Controllers
by Sanoj Kumar, Harendra Pal Singh, Musrrat Ali and Abdul Rahaman Wahab Sait
Fractal Fract. 2025, 9(12), 759; https://doi.org/10.3390/fractalfract9120759 - 23 Nov 2025
Viewed by 524
Abstract
Seismic-induced vibration mitigation in multi-degree-of-freedom (MDOF) building structures calls for efficient and adaptive control strategies. Fractional-order PIλDμ controllers allow increased flexibility in tuning when compared with the conventional proportional integral derivative (PID) controllers. However, considering highly dynamic seismic conditions, selecting [...] Read more.
Seismic-induced vibration mitigation in multi-degree-of-freedom (MDOF) building structures calls for efficient and adaptive control strategies. Fractional-order PIλDμ controllers allow increased flexibility in tuning when compared with the conventional proportional integral derivative (PID) controllers. However, considering highly dynamic seismic conditions, selecting their optimal parameters remains challenging. A Particle Swarm Optimization (PSO)-based fractional order controller approach is presented in this paper for the optimal tuning of five key parameters of the PIλDμ controller using a two-story building model subjected to the 1940 El Centro earthquake. The controller structure is formulated using fractional-order calculus, while PSO is utilized to determine optimal gains and fractional orders without prior knowledge about the model. Simulation results indicate that the proposed fractional order proportional integral derivative (FOPID) controller is effective in suppressing structural vibrations, outperforming both classical PID control and the uncontrolled case. It is demonstrated that incorporating intelligent optimization techniques along with fractional-order control can be a promising approach toward enhancing seismic resilience in civil structures. Full article
(This article belongs to the Special Issue Fractional Control Systems and Estimation: Control, State Observers and Parameter Estimation)
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34 pages, 8174 KB  
Article
Formation Control of Underactuated AUVs Based on Event-Triggered Communication and Fractional-Order Sliding Mode Control
by Long He, Ya Zhang, Shizhong Li, Bo Li, Mengting Xie, Zehui Yuan and Chenrui Bai
Fractal Fract. 2025, 9(12), 755; https://doi.org/10.3390/fractalfract9120755 - 21 Nov 2025
Viewed by 641
Abstract
To address the challenges faced by multiple autonomous underwater vehicles (AUVs) in formation control under complex marine environments—such as model uncertainties, external disturbances, dynamic communication topology variations, and limited communication resources—this paper proposes an integrated control framework that combines robust individual control, distributed [...] Read more.
To address the challenges faced by multiple autonomous underwater vehicles (AUVs) in formation control under complex marine environments—such as model uncertainties, external disturbances, dynamic communication topology variations, and limited communication resources—this paper proposes an integrated control framework that combines robust individual control, distributed cooperative formation, and dynamic event-triggered communication. At the individual control level, a robust control method based on a fractional-order sliding mode observer (FOSMO) and a fractional-order terminal sliding mode controller (FOTSMC) is developed. The observer exploits the memory and broadband characteristics of fractional calculus to achieve high-precision estimation of lumped disturbances, while the controller constructs a non-integer-order sliding surface with an adaptive gain law to guarantee finite-time convergence of tracking errors. At the formation coordination level, a distributed trajectory generation method based on dynamic consensus is proposed to achieve reference trajectory planning and formation maintenance in a cooperative manner. At the communication level, a dynamic-threshold event-triggered mechanism is designed, where the triggering condition is adaptively adjusted according to the state errors, thereby significantly reducing communication load and energy consumption. Theoretically, Lyapunov-based analysis rigorously proves the stability and convergence of the closed-loop system. Numerical simulations confirm that the proposed method outperforms several benchmark algorithms in terms of tracking accuracy and disturbance rejection. Moreover, the integrated framework maintains precise formation under communication topology variations, achieving a communication reduction rate exceeding 65% compared to periodic protocols while preserving coordination accuracy. Full article
(This article belongs to the Special Issue Fractional Control Systems and Estimation: Control, State Observers and Parameter Estimation)
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22 pages, 14847 KB  
Article
Formation Control of Underactuated AUVs Using a Fractional-Order Sliding Mode Observer
by Long He, Mengting Xie, Ya Zhang, Shizhong Li, Bo Li, Zehui Yuan and Chenrui Bai
Fractal Fract. 2025, 9(7), 465; https://doi.org/10.3390/fractalfract9070465 - 18 Jul 2025
Cited by 2 | Viewed by 1033
Abstract
This paper proposes a control method that combines a fractional-order sliding mode observer and a cooperative control strategy to address the problem of path-following for underactuated autonomous underwater vehicles (AUVs) in complex marine environments. First, a fractional-order sliding mode observer is designed, combining [...] Read more.
This paper proposes a control method that combines a fractional-order sliding mode observer and a cooperative control strategy to address the problem of path-following for underactuated autonomous underwater vehicles (AUVs) in complex marine environments. First, a fractional-order sliding mode observer is designed, combining fractional calculus and double-power convergence laws to enhance the estimation accuracy of high-frequency disturbances. An adaptive gain mechanism is introduced to avoid dependence on the upper bound of disturbances. Second, a formation cooperative control strategy based on path parameter coordination is proposed. By setting independent reference points for each AUV and exchanging path parameters, formation consistency is achieved with low communication overhead. For the followers’ speed control problem, an error-based expected speed adjustment mechanism is introduced, and a hyperbolic tangent function is used to replace the traditional arctangent function to improve the response speed of the system. Numerical simulation results show that this control method performs well in terms of path-following accuracy, formation maintenance capability, and disturbance suppression, verifying its effectiveness and robustness in complex marine environments. Full article
(This article belongs to the Special Issue Fractional Control Systems and Estimation: Control, State Observers and Parameter Estimation)
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25 pages, 1530 KB  
Article
Adaptive Fractional Order Control for Bispectral Index Regulation During Anaesthesia
by Alin-Ciprian Malița, Cristina Ioana Muresan, Manuel A. Duarte-Mermoud and Gustavo Ceballos Benavides
Fractal Fract. 2025, 9(6), 330; https://doi.org/10.3390/fractalfract9060330 - 22 May 2025
Cited by 2 | Viewed by 1772
Abstract
Human error remains a significant concern in the medical field, particularly in anaesthesia, where even minor miscalculations can jeopardise patient safety. To address these challenges, the integration of automated control systems has emerged as a viable solution. Most existing control algorithms are tuned [...] Read more.
Human error remains a significant concern in the medical field, particularly in anaesthesia, where even minor miscalculations can jeopardise patient safety. To address these challenges, the integration of automated control systems has emerged as a viable solution. Most existing control algorithms are tuned using a nominal patient model and inter-patient variability is tackled by incorporating robustness in the controller design. A personalised approach is, however, desirable. In this paper, a hybrid control framework that combines fractional-order control with a model-reference adaptive control (MRAC) approach is proposed as a solution for personalised control of the bispectral index (BIS). The system is designed to meet stringent performance requirements while ensuring stability and robustness. Comparative result with a non-adaptive fractional order controller are presented to demonstrate the efficiency of the proposed adaptive strategy. Simulation results demonstrate promising outcomes, both with respect to the selected criteria and in alignment with the anticipated future developments. Full article
(This article belongs to the Special Issue Fractional Control Systems and Estimation: Control, State Observers and Parameter Estimation)
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24 pages, 5721 KB  
Article
Design, Tuning, and Experimental Validation of Switched Fractional-Order PID Controllers for an Inverted Pendulum System
by Matias Fernández-Jorquera, Marco Zepeda-Rabanal, Norelys Aguila-Camacho and Lisbel Bárzaga-Martell
Fractal Fract. 2025, 9(4), 234; https://doi.org/10.3390/fractalfract9040234 - 8 Apr 2025
Cited by 2 | Viewed by 1370
Abstract
Stabilizing inverted pendulum systems remains a challenging and open control problem due to their inherent instability and relevance in a wide range of real-world applications, including robotics and aerospace systems. While PID and fractional-order PID (FOPID) controllers offer distinct advantages, they individually suffer [...] Read more.
Stabilizing inverted pendulum systems remains a challenging and open control problem due to their inherent instability and relevance in a wide range of real-world applications, including robotics and aerospace systems. While PID and fractional-order PID (FOPID) controllers offer distinct advantages, they individually suffer from trade-offs between performance and control energy. This paper presents the design, implementation, and experimental validation of a switched SW FOPID-PID controller for the stabilization of an inverted pendulum (InvP) system, aiming to achieve an improved balance between system performance and control energy used. The controller was tuned offline using particle swarm optimization (PSO) and a mathematical model of the system for simulation. Additional PID and FOPID controllers were also designed, tuned and validated for comparison purposes. Their performance was assessed through key indicators, including ITAE, ISI, settling time, peak values, and variance and compared against a manufacturer-provided PID controller. The experimental results demonstrated that all three designed controllers outperformed the manufacturer’s PID under nominal conditions. The SW FOPID-PID controller achieved the best overall performance, balancing control energy efficiency and response quality. Under external disturbances, the FOPID and SW FOPID-PID controllers exhibited superior robustness, with the switched controller being the most effective, responding quickly to disturbances while minimizing positional and angular errors. Still, this research is limited to a specific plant and switching strategy; thus, further validation on other systems and switching criteria is necessary to generalize these findings. Full article
(This article belongs to the Special Issue Fractional Control Systems and Estimation: Control, State Observers and Parameter Estimation)
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