Pub Date : 2023-07-20DOI: 10.24425/acs.2021.137420
S. Kazhikenova
The article presents ε -approximation of hydrodynamics equations’ stationary model along with the proof of a theorem about existence of a hydrodynamics equations’ strongly generalized solution. It was proved by a theorem on the existence of uniqueness of the hydrodynamics equations’ temperature model’s solution, taking into account energy dissipation. There was implemented the Galerkin method to study the Navier–Stokes equations, which provides the study of the boundary value problems correctness for an incompressible viscous flow both numerically and analytically. Approximations of stationary and non-stationary models of the hydrodynamics equations were constructed by a system of Cauchy–Kovalevsky equations with a small parameter ε . There was developed an algorithm for numerical modelling of the Navier– Stokes equations by the finite difference method.
{"title":"The unique solvability of stationary and non-stationary incompressible melt models in the case of their linearization","authors":"S. Kazhikenova","doi":"10.24425/acs.2021.137420","DOIUrl":"https://doi.org/10.24425/acs.2021.137420","url":null,"abstract":"The article presents ε -approximation of hydrodynamics equations’ stationary model along with the proof of a theorem about existence of a hydrodynamics equations’ strongly generalized solution. It was proved by a theorem on the existence of uniqueness of the hydrodynamics equations’ temperature model’s solution, taking into account energy dissipation. There was implemented the Galerkin method to study the Navier–Stokes equations, which provides the study of the boundary value problems correctness for an incompressible viscous flow both numerically and analytically. Approximations of stationary and non-stationary models of the hydrodynamics equations were constructed by a system of Cauchy–Kovalevsky equations with a small parameter ε . There was developed an algorithm for numerical modelling of the Navier– Stokes equations by the finite difference method.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"7 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79301819","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 : 2023-07-20DOI: 10.24425/acs.2021.139734
L. Popescu, Ramona-Maria Dimitrov
A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.
{"title":"Application of maximum principle to optimization of production and storage costs","authors":"L. Popescu, Ramona-Maria Dimitrov","doi":"10.24425/acs.2021.139734","DOIUrl":"https://doi.org/10.24425/acs.2021.139734","url":null,"abstract":"A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"88 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77684191","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 : 2023-07-20DOI: 10.24425/acs.2019.129380
T. Kaczorek
A dynamical system is called positive if its trajectory starting from any nonnegative initial state remains forever in the positive orthant for all nonnegative inputs. An overview of state of the art in positive theory is given in the monographs and papers [1, 2, 6, 11, 12]. Variety of models having positive behavior can be found in engineering, economics, social sciences, biology and medicine. The stability of linear and nonlinear standard and positive fractional systems has been addressed in [3–6, 8, 15, 16, 20–23]. The stabilization of positive descriptor fractional systems has been investigated in [10, 11, 20, 21]. The superstable linear systems have been addressed in [17, 18]. Positive linear systems with different fractional orders have been introduced in [14, 13] and their stability has been analyzed in [3, 20]. The absolute stability of a class of positive nonlinear systems has been investigated in [7]. In this paper the positivity and absolute stability of a class of nonlinear continuous-time and discrete-time systems with nonpositive linear parts will be addressed. The paper is organized as follows. In section 2 some preliminaries concerning positivity and stability of linear systems are recalled. The positivity and absolute stability of positive continuous-time nonlinear systems with nonpositive linear
{"title":"Absolute stability of a class of nonlinear systems with nonpositive linear parts","authors":"T. Kaczorek","doi":"10.24425/acs.2019.129380","DOIUrl":"https://doi.org/10.24425/acs.2019.129380","url":null,"abstract":"A dynamical system is called positive if its trajectory starting from any nonnegative initial state remains forever in the positive orthant for all nonnegative inputs. An overview of state of the art in positive theory is given in the monographs and papers [1, 2, 6, 11, 12]. Variety of models having positive behavior can be found in engineering, economics, social sciences, biology and medicine. The stability of linear and nonlinear standard and positive fractional systems has been addressed in [3–6, 8, 15, 16, 20–23]. The stabilization of positive descriptor fractional systems has been investigated in [10, 11, 20, 21]. The superstable linear systems have been addressed in [17, 18]. Positive linear systems with different fractional orders have been introduced in [14, 13] and their stability has been analyzed in [3, 20]. The absolute stability of a class of positive nonlinear systems has been investigated in [7]. In this paper the positivity and absolute stability of a class of nonlinear continuous-time and discrete-time systems with nonpositive linear parts will be addressed. The paper is organized as follows. In section 2 some preliminaries concerning positivity and stability of linear systems are recalled. The positivity and absolute stability of positive continuous-time nonlinear systems with nonpositive linear","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"49 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77239575","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 : 2023-07-20DOI: 10.24425/acs.2019.129385
Adnan Daraghmeh, N. Qatanani
In this article we focus on the balanced truncation linear quadratic regulator (LQR) with constrained states and inputs. For closed-loop, we want to use the LQR to find an optimal control that minimizes the objective function which called “the quadratic cost function” with respect to the constraints on the states and the control input. In order to do that we have used formal asymptotes for the Pontryagin maximum principle (PMP) and we introduce an approach using the so called The Hamiltonian Function and the underlying algebraic Riccati equation. The theoretical results are validated numerically to show that the model order reduction based on open-loop balancing can also give good closed-loop performance.
{"title":"Numerical error bound of optimal control for homogeneous linear systems","authors":"Adnan Daraghmeh, N. Qatanani","doi":"10.24425/acs.2019.129385","DOIUrl":"https://doi.org/10.24425/acs.2019.129385","url":null,"abstract":"In this article we focus on the balanced truncation linear quadratic regulator (LQR) with constrained states and inputs. For closed-loop, we want to use the LQR to find an optimal control that minimizes the objective function which called “the quadratic cost function” with respect to the constraints on the states and the control input. In order to do that we have used formal asymptotes for the Pontryagin maximum principle (PMP) and we introduce an approach using the so called The Hamiltonian Function and the underlying algebraic Riccati equation. The theoretical results are validated numerically to show that the model order reduction based on open-loop balancing can also give good closed-loop performance.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"99 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73169029","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 : 2023-07-20DOI: 10.24425/acs.2022.141720
{"title":"Linguistic q-rung orthopair fuzzy prioritized aggregation operators based on Hamacher t-norm and t-conorm and their applications to multicriteria group decision making","authors":"","doi":"10.24425/acs.2022.141720","DOIUrl":"https://doi.org/10.24425/acs.2022.141720","url":null,"abstract":"","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"12 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76002626","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 : 2023-07-20DOI: 10.24425/ACS.2019.127529
T. Kaczorek
A dynamical system is called positive if its trajectory starting from any nonnegative initial state remains forever in the positive orthant for all nonnegative inputs. An overview of state of the art in positive theory is given in the monographs and papers [1, 2, 6, 10, 11]. Variety of models having positive behavior can be found in engineering, economics, social sciences, biology and medicine. The stability of linear and nonlinear standard and positive fractional systems has been addressed in [3–8, 14, 15, 19–22]. The stabilization of positive descriptor fractional systems has been investigated in [9, 18, 19, 20]. The superstable linear systems have been addressed in [16, 17]. Positive linear systems with different fractional orders have been introduced in [13, 12] and their stability has been analyzed in [3, 19]. In this paper the positivity and absolute stability of a class of nonlinear continuous-time and discrete-time systems will be investigated. The paper is organized as follows. In section 2 some preliminaries concerning positivity and stability of linear systems are recalled. The positivity and absolute stability of positive continuous-time nonlinear systems is investigated in section 3 and of positive discrete-time nonlinear systems in section 4. Concluding remarks are given in section 5.
{"title":"Absolute stability of a class of positive nonlinear continuous-time and discrete-time systems","authors":"T. Kaczorek","doi":"10.24425/ACS.2019.127529","DOIUrl":"https://doi.org/10.24425/ACS.2019.127529","url":null,"abstract":"A dynamical system is called positive if its trajectory starting from any nonnegative initial state remains forever in the positive orthant for all nonnegative inputs. An overview of state of the art in positive theory is given in the monographs and papers [1, 2, 6, 10, 11]. Variety of models having positive behavior can be found in engineering, economics, social sciences, biology and medicine. The stability of linear and nonlinear standard and positive fractional systems has been addressed in [3–8, 14, 15, 19–22]. The stabilization of positive descriptor fractional systems has been investigated in [9, 18, 19, 20]. The superstable linear systems have been addressed in [16, 17]. Positive linear systems with different fractional orders have been introduced in [13, 12] and their stability has been analyzed in [3, 19]. In this paper the positivity and absolute stability of a class of nonlinear continuous-time and discrete-time systems will be investigated. The paper is organized as follows. In section 2 some preliminaries concerning positivity and stability of linear systems are recalled. The positivity and absolute stability of positive continuous-time nonlinear systems is investigated in section 3 and of positive discrete-time nonlinear systems in section 4. Concluding remarks are given in section 5.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"34 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76048923","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 : 2023-07-20DOI: 10.24425/acs.2021.138695
R. Almeida, E. Girejko, Luís Machado, A. Malinowska, Natália Martins
This paper studies an evacuation problem described by a leader-follower model with bounded confidence under predictive mechanisms. We design a control strategy in such a way that agents are guided by a leader, which follows the evacuation path. The proposed evacuation algorithm is based on Model Predictive Control (MPC) that uses the current and the past information of the system to predict future agents’ behaviors. It can be observed that, with MPC method, the leader-following consensus is obtained faster in comparison to the conventional optimal control technique. The effectiveness of the developed MPC evacuation algorithm with respect to different parameters and different time domains is illustrated by numerical examples.
{"title":"Evacuation by leader-follower model with bounded confidence and predictive mechanisms","authors":"R. Almeida, E. Girejko, Luís Machado, A. Malinowska, Natália Martins","doi":"10.24425/acs.2021.138695","DOIUrl":"https://doi.org/10.24425/acs.2021.138695","url":null,"abstract":"This paper studies an evacuation problem described by a leader-follower model with bounded confidence under predictive mechanisms. We design a control strategy in such a way that agents are guided by a leader, which follows the evacuation path. The proposed evacuation algorithm is based on Model Predictive Control (MPC) that uses the current and the past information of the system to predict future agents’ behaviors. It can be observed that, with MPC method, the leader-following consensus is obtained faster in comparison to the conventional optimal control technique. The effectiveness of the developed MPC evacuation algorithm with respect to different parameters and different time domains is illustrated by numerical examples.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"99 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83604897","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 : 2023-07-20DOI: 10.24425/ACS.2019.131226
J. Klamka, A. Khurshudyan
The constrained averaged controllability of linear one-dimensional heat equation defined on R and R+ is studied. The control is carried out by means of the time-dependent intensity of a heat source located at an uncertain interval of the corresponding domain, the end-points of which are considered as uniformly distributed random variables. Employing the Green’s function approach, it is shown that the heat equation is not constrained averaged controllable neither in R nor in R. Sufficient conditions on initial and terminal data for the averaged exact and approximate controllabilities are obtained. However, constrained averaged controllability of the heat equation is established in the case of point heat source, the location of which is considered as a uniformly distributed random variable. Moreover, it is obtained that the lack of averaged controllability occurs for random variables with arbitrary symmetric density function.
{"title":"Averaged controllability of heat equation in unbounded domains with random geometry and location of controls: The Green’s function approach","authors":"J. Klamka, A. Khurshudyan","doi":"10.24425/ACS.2019.131226","DOIUrl":"https://doi.org/10.24425/ACS.2019.131226","url":null,"abstract":"The constrained averaged controllability of linear one-dimensional heat equation defined on R and R+ is studied. The control is carried out by means of the time-dependent intensity of a heat source located at an uncertain interval of the corresponding domain, the end-points of which are considered as uniformly distributed random variables. Employing the Green’s function approach, it is shown that the heat equation is not constrained averaged controllable neither in R nor in R. Sufficient conditions on initial and terminal data for the averaged exact and approximate controllabilities are obtained. However, constrained averaged controllability of the heat equation is established in the case of point heat source, the location of which is considered as a uniformly distributed random variable. Moreover, it is obtained that the lack of averaged controllability occurs for random variables with arbitrary symmetric density function.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"20 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90325825","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 : 2023-07-20DOI: 10.24425/acs.2019.131228
E. Jezierski, Piotr Łuczak, Pawel Smyczynski, D. Zarychta
The paper presents the possibilities of teaching a robot controller to perform operations of autonomous segregation of objects differing in features that can be identified using a vision system. Objects can be arranged freely on the robot scene also covered withothers. In the learning phase, a robot operator presents the segregation method by moving subsequent objects held in a human hand, e.g. a red object to container A, a green object to container B, etc. The robot system, after recognizing the idea of segregation that is being done using the vision system, continues this work in an autonomous way, until all identified objects will be removed from robotic scene. There are no restrictions on the dimensions, shapes and placement of containers collecting segregated objects. The developed algorithms were verified on a test bench equipped with two modern robots KUKA LBR iiwa 14 R820.
{"title":"Human–robot cooperation in sorting of randomly distributed objects","authors":"E. Jezierski, Piotr Łuczak, Pawel Smyczynski, D. Zarychta","doi":"10.24425/acs.2019.131228","DOIUrl":"https://doi.org/10.24425/acs.2019.131228","url":null,"abstract":"The paper presents the possibilities of teaching a robot controller to perform operations of autonomous segregation of objects differing in features that can be identified using a vision system. Objects can be arranged freely on the robot scene also covered withothers. In the learning phase, a robot operator presents the segregation method by moving subsequent objects held in a human hand, e.g. a red object to container A, a green object to container B, etc. The robot system, after recognizing the idea of segregation that is being done using the vision system, continues this work in an autonomous way, until all identified objects will be removed from robotic scene. There are no restrictions on the dimensions, shapes and placement of containers collecting segregated objects. The developed algorithms were verified on a test bench equipped with two modern robots KUKA LBR iiwa 14 R820.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"40 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77976687","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 : 2023-07-20DOI: 10.24425/acs.2020.133497
{"title":"On a finding the coefficient of one nonlinear wave equation in the mixed problem","authors":"","doi":"10.24425/acs.2020.133497","DOIUrl":"https://doi.org/10.24425/acs.2020.133497","url":null,"abstract":"","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76408664","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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