Pub Date : 2024-07-04DOI: 10.24425/acs.2024.149661
S. Yusubov, Eilmhan N. Mahmudov
In this paper, we study the modern mathematical theory of the optimal control problem associated with the fractional Roesser model and described by Caputo partial derivatives, where the functional is given by the Riemann-Liouville fractional integral. In the formulated problem, a new version of the increment method is applied, which uses the concept of an adjoint integral equation. Using the Banach fixed point principle, we prove the existence and uniqueness of a solution to the adjoint problem. Then the necessary and sufficient optimality condition is derived in the form of the Pontryagin’s maximum principle. Finally, the result obtained is illustrated by a concrete example.
{"title":"Pontryagin’s maximum principle for the Roesser model with a fractional Caputo derivative","authors":"S. Yusubov, Eilmhan N. Mahmudov","doi":"10.24425/acs.2024.149661","DOIUrl":"https://doi.org/10.24425/acs.2024.149661","url":null,"abstract":"In this paper, we study the modern mathematical theory of the optimal control problem associated with the fractional Roesser model and described by Caputo partial derivatives, where the functional is given by the Riemann-Liouville fractional integral. In the formulated problem, a new version of the increment method is applied, which uses the concept of an adjoint integral equation. Using the Banach fixed point principle, we prove the existence and uniqueness of a solution to the adjoint problem. Then the necessary and sufficient optimality condition is derived in the form of the Pontryagin’s maximum principle. Finally, the result obtained is illustrated by a concrete example.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141677490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-29DOI: 10.24425/acs.2024.149650
Souad Salmi, D. Bouagada
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.
本文考虑了一类新的二维分数线性系统。受干扰系统的稳定半径是根据 H ∞ 规范描述的。用线性矩阵不等式提供了确保闭环系统稳定裕度的充分条件。还考虑了这些系统的 D 稳定区域的概念。我们还提供了一些例子来验证我们主要结果的适用性。
{"title":"Stability margins for generalized fractional two-dimensional state space models","authors":"Souad Salmi, D. Bouagada","doi":"10.24425/acs.2024.149650","DOIUrl":"https://doi.org/10.24425/acs.2024.149650","url":null,"abstract":"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.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-29DOI: 10.24425/acs.2024.149658
Hanna Furmaǹczyk, M. Kubale
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 G◦ lH 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=( G◦ lH) + 1 colors in the remaining cases.
如果一个图 G 的顶点可以被分割成 k 个独立的集合，使得任意两个集合中的顶点数最多相差一个，那么这个图就是等k着色的。存在这种着色的最小整数 k 称为 G 的公平色度数，用 x=( G) 表示。本文研究的问题是确定立方图 G◦ lH 的多重着色的公平色度数值。立方图的多角体的普通着色问题可在多项式时间内求解。对于这些图，公平着色问题的复杂性是一个未决问题。我们提供了一些可在多项式时间内求解的立方体多角形案例，并给出了此类图形的简单线性时间公平着色算法，在其余案例中最多使用 x=( G◦ lH) + 1 种颜色。
{"title":"Equitable colorings of ��-corona products of cubic graphs","authors":"Hanna Furmaǹczyk, M. Kubale","doi":"10.24425/acs.2024.149658","DOIUrl":"https://doi.org/10.24425/acs.2024.149658","url":null,"abstract":"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 G◦ lH 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=( G◦ lH) + 1 colors in the remaining cases.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140366055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-29DOI: 10.24425/acs.2024.149653
Tadeusz Kaczorek, A. Ruszewski
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.
{"title":"The Floquet-Lyapunov transformation for fractional discrete-time linear systems with periodic parameters","authors":"Tadeusz Kaczorek, A. Ruszewski","doi":"10.24425/acs.2024.149653","DOIUrl":"https://doi.org/10.24425/acs.2024.149653","url":null,"abstract":"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.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-29DOI: 10.24425/acs.2024.149654
S. Korczak
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).
{"title":"Caster Car – underactuated ground vehicle with caster wheels","authors":"S. Korczak","doi":"10.24425/acs.2024.149654","DOIUrl":"https://doi.org/10.24425/acs.2024.149654","url":null,"abstract":"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).","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-29DOI: 10.24425/acs.2024.149652
A. Ganie, Debashis Dutta
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.
{"title":"A spherical fuzzy correlation coefficient based on statistical viewpoint with its applications in classification and bidirectional approximate reasoning","authors":"A. Ganie, Debashis Dutta","doi":"10.24425/acs.2024.149652","DOIUrl":"https://doi.org/10.24425/acs.2024.149652","url":null,"abstract":"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.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-29DOI: 10.24425/acs.2024.149656
S. Al-Azzawi
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.
{"title":"Dynamical behavior of a new jerk system inspired from chaotic memory oscillators","authors":"S. Al-Azzawi","doi":"10.24425/acs.2024.149656","DOIUrl":"https://doi.org/10.24425/acs.2024.149656","url":null,"abstract":"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.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-29DOI: 10.24425/acs.2024.149659
Qiang Wang, Yinghui Huang
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.
{"title":"Novel path planning method using marine predator algorithm for mobile robot","authors":"Qiang Wang, Yinghui Huang","doi":"10.24425/acs.2024.149659","DOIUrl":"https://doi.org/10.24425/acs.2024.149659","url":null,"abstract":"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.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-29DOI: 10.24425/acs.2024.149655
Chahrazed Boudefla, Selma Baghli-Bendimerad
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.
{"title":"Nonlocal controllability of mild solutions for neutral evolution equations with state-dependent delay in Fréchet spaces","authors":"Chahrazed Boudefla, Selma Baghli-Bendimerad","doi":"10.24425/acs.2024.149655","DOIUrl":"https://doi.org/10.24425/acs.2024.149655","url":null,"abstract":"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.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140365930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-29DOI: 10.24425/acs.2024.149657
Xue Feng, Shifeng Liu, Wuhuan Xu
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.
{"title":"A new multi-attribute group decision-making method based on probabilistic multi-valued linguistic spherical fuzzy sets for the site selection of charging piles","authors":"Xue Feng, Shifeng Liu, Wuhuan Xu","doi":"10.24425/acs.2024.149657","DOIUrl":"https://doi.org/10.24425/acs.2024.149657","url":null,"abstract":"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.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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