Observability and Observer Design of Fractional-Order Nonlinear Systems

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

Deadline for manuscript submissions: closed (15 May 2024) | Viewed by 1672

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Department of Physics and Mathematics, Universidad Iberoamericana, Ciudad de México 01219, Mexico
Interests: fractional calculus; linear systems theory; transport phenomena; condensed matter physics; control theory; nonlinear analysis
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Instituto Nacional de Astrofisica Optica y Electronica, Puebla, Mexico
Interests: fractional-order systems; Lyapunov stability theory for fractional-order systems; chaotic systems; nonlinear observers for integer and fractional-order systems

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Department of Multidisciplinay Engineering, Texas A&M University, 6200 Tres Lagos Blvd, Higher Education Center at McAllen, McAllen, TX 78504, USA
Interests: fractional calculus; nonlinear systems; robotics; fuzzy logics; neural networks; control theory; integral equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The state of a dynamical system consists in the information that, together with the input, uniquely determines the output. In many cases, research on control theory is carried out under the supposition that the whole state is known by means of external measurements using a sensor. However, it is well known that one can use fewer sensors than there are states of systems due to economic costs or technological limitations. One of the more famous solutions to this problem is the design of algorithms of estimation or observers, i.e., dynamical systems capable of estimating internal information from measurements of the available input and output of that system. To encompass as much as possible all the properties of the system dynamics and to obtain more accurate and flexible structures, research has been conducted employing different modeling approaches using fractional calculus. Fractional calculus is a generalization of conventional integer-order calculus employing integrodifferential operators, for example, Caputo, Riemann–Liouville, Atangana–Baleanu, or Caputo–Fabrizio. Further generalizations are possible with Prabhakar fractional operators, Sonine-like generalized operators, and conformable and distributed-order derivatives.

This Special Issue addresses the newest developments in nonlinear observers’ theory of fractional-order systems modeled with different integrodifferential operators, convergence analysis utilizing the Lyapunov approach, observability properties of certain classes of nonlinear fractional-order systems, state reconstruction design by means of asymptotic and finite-time observers, observer-based controllers, separation principles in fractional systems, synchronization, and fault estimation.

Prof. Dr. Guillermo Fernández-Anaya
Dr. Oscar Martínez-Fuentes
Dr. Aldo Jonathan Muñoz-Vazquez
Guest Editors

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Keywords

  • nonlinear observers
  • fractional differential equations
  • generalized calculus
  • observer theory
  • fault detection
  • synchronization
  • observer-based controllers

Published Papers (1 paper)

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15 pages, 1132 KiB  
Article
Uncertainty Observer-Based Control for a Class of Fractional- Order Non-Linear Systems with Non-Linear Control Inputs
by Juan Javier Montesinos-García, Jorge Luis Barahona-Avalos, Jesús Linares-Flores and José Antonio Juárez-Abad
Fractal Fract. 2023, 7(12), 836; https://doi.org/10.3390/fractalfract7120836 - 25 Nov 2023
Cited by 1 | Viewed by 921
Abstract
This paper presents a novel control strategy based on an uncertainty estimator for a class of fractional-order nonlinear systems characterized by a polynomial input. The proposed strategy allows the system to be controlled without resorting to transformations or approximate linearization. This is accomplished [...] Read more.
This paper presents a novel control strategy based on an uncertainty estimator for a class of fractional-order nonlinear systems characterized by a polynomial input. The proposed strategy allows the system to be controlled without resorting to transformations or approximate linearization. This is accomplished by using a fractional-order sliding-mode observer, whose task is to estimate certain portions of the state of the nonlinear system of a non-integer order, thus allowing the control law to counteract these elements to steer the system towards a desired behavior. To validate the performance of the proposed strategy, it was implemented, both in simulation and experimentally, to regulate the temperature of the cold side of a thermoelectric module fed by a DC/DC electronic power converter of the step-down type, a system that is known to have a nonlinear polynomial-type control input. Full article
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