Applied sciences

Archives of Control Sciences

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Archives of Control Sciences | 2023 | vol. 33 | No 1

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Abstract

Differential geometry is a strong and highly effective mathematical subject for robot gripper design when grasping within the predetermined trajectories of path planning. This study in grasping focuses on differential geometry analysis utilizing the Lie algebra, geodesic, and Riemann Curvature Tensors (RCT). The novelty of this article for 2RR robot mechanisms lies in the approach of the body coordinate with the geodesic and RCT. The importance of this research is significant especially in grasping and regrasping objects with varied shapes. In this article, the types of workspaces are clarified and classified for grasping and regrasping kinematics.
The regrasp has not been sufficiently investigated of body coordinate systems in Lie algebra. The reason for this is the difficulty in understanding relative coordinates in Lie algebra via the body coordinate system. The complexity of the equations has not allowed many researchers to overcome this challenge. The symbolic mathematics toolbox in the Maxima, on the other hand, aided in the systematic formulation of the workspaces in Lie algebra with geodesic and RCT.
The Lie algebra se(3) equations presented here have already been developed for robot kinematics from many references. These equations will be used to derive the followingworkspace types for grasping and regrasping. Body coordinate workspace, spatial coordinate workspace with constraints, body coordinate workspace with constraints, spatial coordinate workspace with constraints are the workspace types. The RCT and geodesic solutions exploit these four fundamental workspace equations derived using Lie algebra.
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Authors and Affiliations

Haydar Sahin
1

  1. Istanbul Gedik University, Engineering Faculty, Mechatronics Engineering Department, Istanbul, Türkiye
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Abstract

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced for triangular wave non-linearity. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
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Authors and Affiliations

Rasappan Suresh
1
Kumaravel Sathish Kumar
2
Murugesan Regan
2
K.A. Niranjan Kumar
2
R. Narmada Devi
2
Ahmed J. Obaid
3

  1. Mathematics Section, Department of Information Technology, College of Computing and Information Sciences, University of Technology and Applied Sciences, Ibri, Sultanate of Oman
  2. Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R& D Institute of Science and Technology, Avadi, Chennai-62, India
  3. Faculty of Computer Science and Mathematics, University of Kufa, Iraq
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Abstract

This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.
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Authors and Affiliations

Imed Basdouri
1
ORCID: ORCID
Souad Kasmi
2
Jean Lerbet
3

  1. Gafsa University, Faculty of Sciences of Gafsa, Department of Mathematics, Zarroug Gafsa 2112 Tunisia
  2. Sfax University, Faculty of Sciences of Sfax, Department of Mathematics, BP 1171 Sfax 3000 Tunisia
  3. Laboratoire de Mathématiques et de Modélisation d’Evry, Univ d’Evry, Université Paris Saclay, France
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Abstract

The asymptotic stability of fractional positive descriptor continuous-time and discretetime linear systems is considered. New sufficient conditions for stability of fractional positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of fractional continuous-time and discrete-time linear systems.
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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID
Andrzej Ruszewski
1
ORCID: ORCID

  1. Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
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Abstract

Generalized observers are proposed to relax the existing conditions required to design Luenberger observers for rectangular linear descriptor systems with unknown inputs. The current work is focused on designing index one generalized observers, which can be naturally extended to higher indexes. Sufficient conditions in terms of system operators for the existence of generalized observers are given and proved. Orthogonal transformations are used to derive the results. A physical model is presented to show the usefulness of the proposed theory.
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Authors and Affiliations

Abhinav Kumar
1
Mahendra Kumar Gupta
1 2

  1. Department of Mathematics, National Institute of Technology Jamshedpur, Jharkhand, India
  2. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Argul, Khordha, Odisha, 752050 – India
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Abstract

Extremal problems for multiple time delay hyperbolic systems are presented. The optimal boundary control problems for hyperbolic systems in which multiple time delays appear both in the state equations and in theNeumann boundary conditions are solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.
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Authors and Affiliations

Adam Kowalewski
1

  1. AGH University of Science and Technology, Institute of Automatic Control and Robotics, 30-059 Cracow, al. Mickiewicza 30, Poland
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Abstract

In this work, we report a new chaotic population biology system with one prey and two predators. Our new chaotic population model is derived by introducing two nonlinear interaction terms between the prey and predator-2 to the Samardzija-Greller population biology system (1988).We show that the new chaotic population biology system has a greater value of Maximal Lyapunov Exponent (MLE) than the Maximal Lyapunov Exponent (MLE) of the Samardzija- Greller population biology system (1988).We carry out a detailed bifurcation analysis of the new chaotic population biology system with one prey and two predators. We also show that the new chaotic population biology model exhibits multistability with coexisting chaotic attractors. Next, we use the integral sliding mode control (ISMC) for the complete synchronization of the new chaotic population biology system with itself, taken as the master and slave chaotic population biology systems. Finally, for practical use of the new chaotic population biology system, we design an electronic circuit design using Multisim (Version 14.0).
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Authors and Affiliations

Sundarapandian Vaidyanathan
1
Khaled Benkouider
2
Aceng Sambas
3
P. Darwin
4

  1. Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600092, Tamil Nadu, India
  2. Non Destructive Testing Laboratory, Automatic Department, Jijel University, BP 98, 18000, Jijel, Algeria
  3. Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196, West Java, Indonesia
  4. Department of Computer Science and Engineering, Rajalakshmi Institute of Technology, Kuthambakkam, Chennai-600 124, Tamil Nadu, India
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Abstract

In the paper finite-dimensional semilinear dynamical control systems described by fractional-order state equations with the Hilfer fractional derivative are discussed. The formula for a solution of the considered systems is presented and derived using the Laplace transform. Bounded nonlinear function �� depending on a state and controls is used. New sufficient conditions for controllability without constraints are formulated and proved using Rothe’s fixed point theorem and the generalized Darbo fixed point theorem. Moreover, the stability property is used to formulate constrained controllability criteria. An illustrative example is presented to give the reader an idea of the theoretical results obtained. A transient process in an electrical circuit described by a system of Hilfer type fractional differential equations is proposed as a possible application of the study.
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Authors and Affiliations

Beata Sikora
1
ORCID: ORCID

  1. Department of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
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Abstract

Spherical fuzzy sets (SFSs) provide more free space for decision makers (DMs) to express preference information from four aspects: approval, objection, abstention and refusal. The partitioned Maclaurin symmetric mean (PMSM) operator is an effective information fusion tool, which can fully capture the interrelationships among any multiple attributes in the same block whereas attributes in different block are unrelated. Therefore, in this paper,we first extendPMSM operator to spherical fuzzy environment and develop spherical fuzzy PMSM (SFPMSM) operator as well as spherical fuzzy weighted PMSM (SFWPMSM) operator. Meanwhile, we discuss some properties and special cases of these two operators. To diminish the impact of extreme evaluation values on decision-making results, then we integrate power average (PA) operator and PMSM operator to further develop spherical fuzzy power PMSM (SFPPMSM) operator and spherical fuzzy weighted power PMSM (SFWPPMSM) operator and also investigate their desirable properties. Subsequently, a new multiple attribute group decision making (MAGDM) method is established based on SFWPPMSM operator under spherical fuzzy environment. Finally, two numerical examples are used to illustrate the proposed method, and comparative analysis with the existing methods to further testy the validity and superiority of the proposed method.
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Authors and Affiliations

Huiyuan Zhang
1 2
Qiang Cai
3
Guiwu Wei
4 3

  1. School of Mathematics and Statistics, Liupanshui Normal University, Liupanshui 553004, Guizhou, P.R. China
  2. School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610101, P.R. China
  3. School of Business, Sichuan Normal University, Chengdu, 610101, P.R. China
  4. School of Mathematical Sciences, Sichuan NormalUniversity, Chengdu, 610101, P.R. China
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Abstract

This study investigates Thomas’ cyclically symmetric attractor dynamics with mathematical and electronic simulations using a proportional fractional derivative to comprehend the dynamics of a given chaotic system. The three-dimensional chaotic flow was examined in detail with Riemann-Liouville derivative for different values of the fractional index to highlight the sensitivity of chaotic systems with initial conditions. Thus, the dynamics of the fractional index system were investigated with Eigenvalues, Kaplan–Yorke dimension, Lyapunov exponent, and NIST testing, and their corresponding trajectories were visualized with phase portraits, 2D density plot, and Poincaré maps. After obtaining the results, we found that the integer index dynamics are more complex than the fractional index dynamics. Furthermore, the chaotic system circuit is simulated with operational amplifiers for different fractional indices to generate analog signals of the symmetric attractor, making it an important aspect of engineering. The qualitative application of our nonlinear chaotic system is then applied to encrypt different data types such as voice, image, and video, to ensure that the developed nonlinear chaotic system can widely applied in the field of cyber security.
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Authors and Affiliations

NajeebAlam Khan
1
Muhammad Ali Qureshi
2
Saeed Akbar
1
Asmat Ara
3

  1. Department of Mathematics, University of Karachi, Karachi 75270, Pakistan
  2. Department of Physics, University of Karachi, Karachi 75270, Pakistan
  3. College of Humanities and Sciences, PAF-KIET, Karachi 75190, Pakistan

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