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Dynamical Systems and Their Applications (DSTA) — In Memory of Prof. Dr. José A. Tenreiro Machado

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 6733

Special Issue Editors

Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200–465 Porto, Portugal
Interests: complex systems modelling; automation and robotics; fractional order systems modelling and control; data analysis and visualization
Special Issues, Collections and Topics in MDPI journals
Engineering School (DEIM), University of Tuscia, Largo dell'Università, 01100 Viterbo, Italy
Interests: wavelets; fractals; fractional and stochastic equations; numerical and computational methods; mathematical physics; nonlinear systems; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

In Memory of Prof. J. A. Tenreiro Machado

On October 6, 2021 Prof. Tenreiro Machado passed away. With his kindness, his warm character and his sophisticated sense of humor, Prof. Tenreiro Machado had a reassuring presence, which helped the flow of exchanges at all levels. His passion for science seemed to be boundless. He was always eager to embark on new projects and to contaminate others with his enthusiasm.

Prof. Tenreiro Machado had a great cultural background and very extensive scientific interests. He was a pioneer in the field of fractional calculus. The breadth of Prof. Tenreiro Machado’s research, the global dissemination of his results, and his legacy belong to all scholars involved in any way in the study of fractional calculus.

His innovative mathematical ideas and contributions will certainly serve as an inspiration for mathematicians for a long time.

We are proud that he was the Editor-in-Chief of Mathematics and Section Editor-in-Chief of Entropy when this Special Issue was proposed. We dedicate this Special Issue to his memory. We are unable to express our sadness for this loss.

Dear Colleagues,

The theory of dynamical systems has evolved from linear to nonlinear and then to complex systems. Indeed, new modelling and control techniques have been developed and applied in various fields, such as physics, mechanics, electronics, economy, finance, geophysics and biology to mention a few. Nonlinear and complex dynamical systems, as well as their related concepts of chaos, bifurcations, criticality, symmetry, memory, scale invariance, fractality, fractionality and other rich features, have attracted researchers from many areas of science and technology that are involved in systems modelling and control, with applications to real-world problems. However, at present, there are still many unsolved problems, and new theoretical developments and applications are needed in order to describe and control more accurately dynamical systems with linear, nonlinear and complex behaviour.

This Special Issue focuses on the modelling and control of dynamic systems. Manuscripts on linear and nonlinear dynamics, systems modelling, advanced control theory, complex systems, fractional calculus, fractals, entropy, information theory, chaos, self-organization and criticality, among others, are welcome.

This Special Issue will bring together contributions from researchers in different topics of engineering, mathematics, physics, biology, geophysics and other sciences. Papers describing original theoretical research as well as new experimental results are welcome.

You may choose our Joint Special Issue in Mathematics.

Prof. Dr. Alexandra M.S.F. Galhano
Prof. Dr. António Lopes
Prof. Dr. Carlo Cattani
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 100 words) can be sent to the Editorial Office for announcement on this website.

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. Entropy 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 2600 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

  • complex systems
  • linear and nonlinear dynamics
  • advanced control theory
  • fractional calculus
  • fractals
  • entropy
  • information theory

Related Special Issue

Published Papers (5 papers)

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Research

18 pages, 1255 KiB  
Article
LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach
Entropy 2022, 24(10), 1496; https://doi.org/10.3390/e24101496 - 19 Oct 2022
Cited by 3 | Viewed by 1306
Abstract
In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional–differential output feedback controller to obtain a satisfactory performance. [...] Read more.
In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional–differential output feedback controller to obtain a satisfactory performance. The stability of the overall system is described in terms of matrix inequalities, and the corresponding analysis is performed in the perspective of Lyapunov’s theory. Two application examples verify the analytic findings. Full article
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13 pages, 1312 KiB  
Article
Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method
Entropy 2022, 24(10), 1345; https://doi.org/10.3390/e24101345 - 23 Sep 2022
Viewed by 917
Abstract
This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF [...] Read more.
This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique. Full article
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14 pages, 475 KiB  
Article
Fractional Survival Functional Entropy of Engineering Systems
Entropy 2022, 24(9), 1275; https://doi.org/10.3390/e24091275 - 10 Sep 2022
Cited by 1 | Viewed by 996
Abstract
An alternate measure of uncertainty, termed the fractional generalized cumulative residual entropy, has been introduced in the literature. In this paper, we first investigate some variability properties this measure has and then establish its connection to other dispersion measures. Moreover, we prove under [...] Read more.
An alternate measure of uncertainty, termed the fractional generalized cumulative residual entropy, has been introduced in the literature. In this paper, we first investigate some variability properties this measure has and then establish its connection to other dispersion measures. Moreover, we prove under sufficient conditions that this measure preserves the location-independent riskier order. We then elaborate on the fractional survival functional entropy of coherent and mixed systems’ lifetime in the case that the component lifetimes are dependent and they have identical distributions. Finally, we give some bounds and illustrate the usefulness of the given bounds. Full article
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14 pages, 333 KiB  
Article
Some Further Results on the Fractional Cumulative Entropy
Entropy 2022, 24(8), 1037; https://doi.org/10.3390/e24081037 - 28 Jul 2022
Cited by 2 | Viewed by 1053
Abstract
In this paper, the fractional cumulative entropy is considered to get its further properties and also its developments to dynamic cases. The measure is used to characterize a family of symmetric distributions and also another location family of distributions. The links between the [...] Read more.
In this paper, the fractional cumulative entropy is considered to get its further properties and also its developments to dynamic cases. The measure is used to characterize a family of symmetric distributions and also another location family of distributions. The links between the fractional cumulative entropy and the classical differential entropy and some reliability quantities are also unveiled. In addition, the connection the measure has with the standard deviation is also found. We provide some examples to establish the variability property of this measure. Full article
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7 pages, 227 KiB  
Article
On Positive Definite Kernels of Integral Operators Corresponding to the Boundary Value Problems for Fractional Differential Equations
Entropy 2022, 24(4), 515; https://doi.org/10.3390/e24040515 - 06 Apr 2022
Viewed by 1434
Abstract
In the spectral analysis of operators associated with Sturm–Liouville-type boundary value problems for fractional differential equations, the problem of positive definiteness or the problem of Hermitian nonnegativity of the corresponding kernels plays an important role. The present paper is mainly devoted to this [...] Read more.
In the spectral analysis of operators associated with Sturm–Liouville-type boundary value problems for fractional differential equations, the problem of positive definiteness or the problem of Hermitian nonnegativity of the corresponding kernels plays an important role. The present paper is mainly devoted to this problem. It should be noted that the operators under study are non-self-adjoint, their spectral structure is not well investigated. In this paper we use various methods to prove the Hermitian non-negativity of the studied kernels; in particular, a study of matrices that approximate the Green’s function of the boundary value problem for a differential equation of fractional order is carried out. Using the well-known Livshits theorem, it is shown that the system of eigenfunctions of considered operator is complete in the space L2(0,1). Generally speaking, it should be noted that this very important problem turned out to be very difficult. Full article
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