Nauki Techniczne

Archives of Control Sciences

Zawartość

Archives of Control Sciences | 2024 | vol. 34 | No 1

Abstrakt

This paper investigates the Luenberger observer design problem for non-autonomous control semilinear evolution equations with disturbances in Banach spaces. Then, the practicalstabilization problem of the system is solved, yielding a compensator based on the Luenberger observer by using integral inequalities of the Gronwall type. Sufficient conditions of the controller and observer problem are satisfied, we show that the proposed controller with estimatedstate feedback from the proposed practical Luenberger observer will achieve global practical stabilization. We develop novel ideas and techniques, which present the further development of mathematical control theory. Furthermore, an example is given to show the applicability of our theoretical results.
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Autorzy i Afiliacje

Fatma Badri
1
Hanen Damak
2
Mohamed Ali Hammami
1

  1. Faculty of Sciences of Sfax, Department of Mathematics, Sfax,Tunisia
  2. Preparatory Engineering Institute of Sfax, Departmentof Mathematics, Sfax, Tunisia

Abstrakt

In this paper, a new class of bidimensional fractional linear systems is considered. The stability radius of the disturbed system is described according to the H norm. Sufficient conditions to ensure the stability margins of the closed-loop system are offered in terms of linear matrix inequalities. The concept of D stability region for these systems is also considered. Examples are provided to verify the applicability of our main result.
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Autorzy i Afiliacje

Souad Salmi
1
Djillali Bouagada
2
ORCID: ORCID

  1. Department of Mathematics and ComputerScience, ACSY Team-Laboratory of Pure and Applied Mathematics, Abdelhamid Ibn Badis UniversityMostaganem, P.O.Box 227/118, 27000 Mostaganem, Algeria
  2. National HigherSchool of Mathematics, Scientific and Technology Hub of Sidi Abdellah, ACSY Team-Laboratory of Pureand Applied Mathematics(UMAB), P.O. Box 75, Algiers 16093, Algeria

Abstrakt

Quadcopter unmanned aerial vehicle is a multivariable, coupled, unstable, and underactuated system with inherent nonlinearity. It is gaining popularity in various applications and has been the subject of numerous research studies. However, modelling and controlling a quadcopter to follow a trajectory is a challenging issue for which there is no unique solution. This study proposes an optimal hybrid quadcopter control with MPC-based backstepping control for following a reference trajectory. The outer-loop controller (backstepping controller) regulates the quadcopter’s position, whereas the inner-loop controller (Model Predictive Control) regulates its attitude. The translational and rotational dynamics of the quadcopter are analyzed utilizing the Newton-Euler method. After that, the backstepping controller (BC) is created, which is a recurrent control method according to Lyapunov’s theory that utilizes a genetic algorithm (GA) to choose the controller parameters automatically. In order to apply a linear control technique in the presence of nonlinearities in the quadcopter dynamics, Linear Parameter Varying (LPV) Model Predictive Control (MPC) structure is developed. Simulation validated the dynamic performance of the proposed optimal hybrid MPC-based backstepping controller of the quadcopter in following a given reference trajectory. The simulations demonstrate the fact that using a command control input in trajectory tracking, the proposed control algorithm offers suitable tracking over the assigned position references with maximum appropriate tracking errors of 0.1 m for the �� and �� positions and 0.15 m for the �� position.
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Autorzy i Afiliacje

Solomon C. Nwafor
1
ORCID: ORCID
Joy N. Eneh
2
ORCID: ORCID
Mmasom I. Ndefo
2
ORCID: ORCID
Oluchi C. Ugbe
3
ORCID: ORCID
Henry I. Ugwu
2
ORCID: ORCID
Ozoemena Ani
4
ORCID: ORCID

  1. Department of Mechatronic Engineering,Univeristy of Nigeria, Nsukka, Enugu State, Nigeria
  2. Department of Electronicand Computer Engineering, University of Nigeria, Nsukka, Enugu State, Nigeria
  3. Department of Electrical Engineering, Universityof Nigeria, Nsukka, Enugu State, Nigeria
  4. Department of Mechatronic Engineering and DepartmentofAgricultural and Bioresources Engineering,Univeristy of Nigeria, Nsukka, Enugu State, Nigeria

Abstrakt

Spherical fuzzy sets are more powerful in modelling the uncertain situations than picture fuzzy sets, fermatean fuzzy sets, Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. In this paper, we first define the variance and covariance of spherical fuzzy sets. Then, using variance and covariance, we define the unique spherical fuzzy set correlation metric in line with the statistical coefficient of correlation. Two spherical fuzzy sets are correlated in both direction and strength using the provided measure of correlation. We discussed its many characteristics. We compared the measure of correlation with the current ones through linguistic variables. We established its validity by showing its application in bidirectional approximate reasoning. We also resolve a pattern identification issue in the spherical fuzzy environment using the provided correlation function, and we compare the results with several current measurements.
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Autorzy i Afiliacje

Abdul Haseeb Ganie
1
ORCID: ORCID
Debashis Dutta
1
ORCID: ORCID

  1. Department of Mathematics, National Institute of Technology, Warangal506004, Telangana, India

Abstrakt

The Floquet-Lyapunov transformation is extended to fractional discrete-time linear systems with periodic parameters. A procedure for computation of the transformation is proposed and illustrated by a numerical example.
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Autorzy i Afiliacje

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

Abstrakt

This paper presents a new type of underactuated ground mobile robot called Caster Car. The platform consists of a front-driven and steered wheel and two uncontrolled rear caster wheels. The Caster Car model presented can be an interesting alternative for mobile robots that connects dynamic properties of hovercrafts and classical 4-wheeled cars. Underactuated properties of the Caster Car cause that classical proportional-derivative feedback control give the ability to affect only selected configuration variables. Three mathematical models of the Caster Car are proposed: a dynamic model with free-moving casters, a dynamic model with blocked casters, and a simplified hovercraft description. Models were tested during tracking tasks with demanding trajectory using selective and full-state control. This full state control was based on the computed torque technique with the pseudoinverse operation and proportional-derivative feedback. It gives the ability to suppress unstable behaviors of uncontrolled orientation but in cost of overall effect (higher position errors).
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Autorzy i Afiliacje

Sebastian Korczak
1
ORCID: ORCID

  1. Warsaw University of Technology, ul. Narbutta84, 02-524 Warsaw, Poland

Abstrakt

In this paper, we prove the controllability of mild solutions of neutral functional evolution equations with state-dependent delay and nonlocal conditions. We establish the non local controllability of mild solutions under certain conditions by combining Avramescu’s nonlinear alternative for the sum of compact and contraction operators in Fréchet spaces with semigroup theory.
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Autorzy i Afiliacje

Chahrazed Boudefla
1
ORCID: ORCID
Selma Baghli-Bendimerad
1
ORCID: ORCID

  1. Po. Box 89, Laboratory of Mathematics, Djillali LiabesUniversity of Sidi Bel-Abbès 22000, Algeria

Abstrakt

This paper constructs a six-term new simple 3D jerk system modeled by chaotic model memory oscillators with four parameters that control the behavior. The suitable choice of one of these parameters helps the system describe behavior and attractors. This means that the choice is a parameter of the associated behavior (dissipative or conservative) and attractors (self-excited or hidden). Some features of the equilibrium are observed that are related to the dependence on these parameters, such as saddle-foci, non-hyperbolic, and node-foci. This system is rich in dynamic features including chaotic, quasi-periodic (2-torus), and periodic via the utilization of bifurcation diagrams and Lyapunov spectrum. Finally, a new image encryption algorithm is introduced that utilizes the jerk system. The algorithm is assessed through statistical performance analysis, according to the results of the experiments and security tests, it has been verified that the suggested image encryption algorithm is highly secure and could be a viable option for real-world applications.
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Autorzy i Afiliacje

Saad Fawzi Al-Azzawi
1
ORCID: ORCID

  1. Department of Mathematics, Collegeof Computer Science and Mathematics, University of Mosul, Mosul, Iraq

Abstrakt

Motivated by the concepts of low carbon and environmental protection, electric vehicles have received much attention and become more and more popular all around the world. The expanding demand for electric vehicles has driven the rapid development of the charging pile industry. One of the prominent issues in charging pile industry is to determine their sites, which is a complex decision-making problem. As a matter of factor, the process of charging piles sites selection can be regarded as multi-attribute group decision-making (MAGDM), which is the main topic of this paper. The recently proposed linguistic spherical fuzzy sets (LSFSs) composed of the linguistic membership degree, linguistic abstinence degree and linguistic non-membership degree are powerful tools to express the evaluation information of decision makers (DMs). Based on the concept of LSFSs, we introduce probabilistic multi-valued linguistic spherical fuzzy sets (PMVLSFSs), which can describe DMs’ fuzzy evaluation information in a more refined and accurate way. The operation rules of PMVLSFSs are also developed in this article. To effectively aggregate PMVLSFSs, the probabilistic multi-valued linguistic spherical fuzzy power generalized Maclaurin symmetric mean operator and the probabilistic multi-valued linguistic spherical fuzzy power weighted generalized Maclaurin symmetric mean are put forward. Based on the above aggregation operators, a new method for MAGDM problem with PMVLSFSs is established. Further, a practical case of suitable site selection of charging pile is used to verify the practicability of this method. Lastly, comparative analysis with other methods is performed to illustrate the advantages and stability of proposed method.
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Autorzy i Afiliacje

Xue Feng
1 2
ORCID: ORCID
Shifeng Liu
1
ORCID: ORCID
Wuhuan Xu
3
ORCID: ORCID

  1. School of Economics and Management, Beijing Jiaotong University, Beijing, China
  2. Beijing Logistics Informatics Research Base, Beijing, China
  3. School of Economics and Management, BeihangUniversity, Beijing, China

Abstrakt

A graph G is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest integer k for which such a coloring exists is known as the equitable chromatic number of G and it is denoted by x=( G). In this paper the problem of determining the value of equitable chromatic number for multicoronas of cubic graphs GlH is studied. The problem of ordinary coloring of multicoronas of cubic graphs is solvable in polynomial time. The complexity of equitable coloring problem is an open question for these graphs. We provide some polynomially solvable cases of cubical multicoronas and give simple linear time algorithms for equitable coloring of such graphs which use at most x=( GlH) + 1 colors in the remaining cases.


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Autorzy i Afiliacje

Hanna Furmańczyk
1
ORCID: ORCID
Marek Kubale
2
ORCID: ORCID

  1. Institute of Informatics, University ofGdańsk, Wita Stwosza 57, 80-308 Gdańsk, Poland
  2. Department of Algorithms andSystem Modelling, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland

Abstrakt

The main goal of robot path planning is to design an optimal path for a robot to navigate from its starting point to its goal while avoiding obstacles and optimizing certain criteria. A novel method using marine predator algorithm which is used in the field of robot path planning is presented. The proposed method has two steps. First step is to build a mathematical model of path planning while second step is optimization process using marine predator algorithm. Simulation results show that the proposed method works well and has good performance in different situations. Therefore, this method is an effective method for robot path planning and related applications.
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Autorzy i Afiliacje

Qiang Wang
1
Yinghui Huang
2

  1. College of Electronic and ElectricalEngineering, Bengbu University, Bengbu 233030, China
  2. College of Computer and Information Engineering, Bengbu University, Bengbu233030, China

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