Pub Date : 2023-07-20DOI: 10.24425/ACS.2020.134675
N. Baleghi, M. Shafiei
This paper proposes a design procedure for observer-based controllers of discrete-time switched systems, in the presence of state’s time-delay, nonlinear terms, arbitrary switching signals, and affine parametric uncertainties. The proposed switched observer and the state-feedback controller are designed simultaneously using a set of linear matrix inequalities (LMIs). The stability analysis is performed based on an appropriate Lyapunov–Krasovskii functional with one switched expression, and in the meantime, the sufficient conditions for observer-based stabilization are developed. These conditions are formulated in the form of a feasibility test of a proposed bilinear matrix inequality (BMI) which is a non-convex problem. To make the problem easy to solve, the BMI is transformed into a set of LMIs using the singular value decomposition of output matrices. An important advantage of the proposed method is that the established sufficient conditions depend only on the upper bound of uncertain parameters. Furthermore, in the proposed method, an admissible upper bound for unknown nonlinear terms of the switched system may be calculated using a simple search algorithm. Finally, the efficiency of the proposed controller and the validity of the theoretical results are illustrated through a simulation example.
{"title":"An observer-based controller design for nonlinear discrete-time switched systems with time-delay and affine parametric uncertainty","authors":"N. Baleghi, M. Shafiei","doi":"10.24425/ACS.2020.134675","DOIUrl":"https://doi.org/10.24425/ACS.2020.134675","url":null,"abstract":"This paper proposes a design procedure for observer-based controllers of discrete-time switched systems, in the presence of state’s time-delay, nonlinear terms, arbitrary switching signals, and affine parametric uncertainties. The proposed switched observer and the state-feedback controller are designed simultaneously using a set of linear matrix inequalities (LMIs). The stability analysis is performed based on an appropriate Lyapunov–Krasovskii functional with one switched expression, and in the meantime, the sufficient conditions for observer-based stabilization are developed. These conditions are formulated in the form of a feasibility test of a proposed bilinear matrix inequality (BMI) which is a non-convex problem. To make the problem easy to solve, the BMI is transformed into a set of LMIs using the singular value decomposition of output matrices. An important advantage of the proposed method is that the established sufficient conditions depend only on the upper bound of uncertain parameters. Furthermore, in the proposed method, an admissible upper bound for unknown nonlinear terms of the switched system may be calculated using a simple search algorithm. Finally, the efficiency of the proposed controller and the validity of the theoretical results are illustrated through a simulation example.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"109 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80840560","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.2020.135850
In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.
{"title":"On LQ optimization problem subject to fractional order irregular singular systems","authors":"","doi":"10.24425/acs.2020.135850","DOIUrl":"https://doi.org/10.24425/acs.2020.135850","url":null,"abstract":"In this paper we discuss the linear quadratic (LQ) optimization problem subject to fractional order irregular singular systems. The aim of this paper is to find the control-state pairs satisfying the dynamic constraint of the form a fractional order irregular singular systems such that the LQ objective functional is minimized. The method of solving is to convert such LQ optimization into the standard fractional LQ optimization problem. Under some particularly conditions we find the solution of the problem under consideration.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"4 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90416077","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.2019.130205
A. Ruszewski, A. Ruszewski
The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.
{"title":"Stability of discrete-time fractional linear systems with delays","authors":"A. Ruszewski, A. Ruszewski","doi":"10.24425/acs.2019.130205","DOIUrl":"https://doi.org/10.24425/acs.2019.130205","url":null,"abstract":"The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"69 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86435588","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.2019.131231
J. Duda
In the paper a Lyapunov matrices approach to the parametric optimization problem of a time-delay system with two commensurate delays and a PI-controller is presented. The value of integral quadratic performance index is equal to the value of the Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix. In the paper is presented the example of a scalar system with two delays and a PI controller.
{"title":"The parametric optimization of a system with two delays and a PI controller","authors":"J. Duda","doi":"10.24425/acs.2019.131231","DOIUrl":"https://doi.org/10.24425/acs.2019.131231","url":null,"abstract":"In the paper a Lyapunov matrices approach to the parametric optimization problem of a time-delay system with two commensurate delays and a PI-controller is presented. The value of integral quadratic performance index is equal to the value of the Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix. In the paper is presented the example of a scalar system with two delays and a PI controller.","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":"88629060","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.2021.138697
In this paper, we introduce necessary and sufficient efficiency conditions associated with a class of multiobjective fractional variational control problems governed by geodesic quasiinvex multiple integral functionals and mixed constraints containing m -flow type PDEs. Using the new notion of ( normal ) geodesic efficient solution , under ( ρ, b ) - geodesic quasiinvexity assumptions, we establish sufficient efficiency conditions for a feasible solution.
本文给出了一类包含m流型偏微分方程的测地拟逆多重积分泛函和混合约束的多目标分数变分控制问题的充要条件。利用(正)测地线有效解的新概念，在(ρ， b) -测地线拟invix假设下，建立了可行解的充分效率条件。
{"title":"Efficiency in vector ratio variational control problems involving geodesic quasiinvex multiple integral functionals","authors":"","doi":"10.24425/acs.2021.138697","DOIUrl":"https://doi.org/10.24425/acs.2021.138697","url":null,"abstract":"In this paper, we introduce necessary and sufficient efficiency conditions associated with a class of multiobjective fractional variational control problems governed by geodesic quasiinvex multiple integral functionals and mixed constraints containing m -flow type PDEs. Using the new notion of ( normal ) geodesic efficient solution , under ( ρ, b ) - geodesic quasiinvexity assumptions, we establish sufficient efficiency conditions for a feasible solution.","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":"86977242","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.2022.141715
Dalia Cabada, Katherine Garcia, Cristi D. Guevara, H. Leiva
In this paper we prove the exact controllability of a time varying semilinear system considering non-instantaneous impulses, delay, and nonlocal conditions occurring simultaneously. It is done by using the Rothe’s fixed point theorem together with some sub-linear conditions on the nonlinear term, the impulsive functions, and the function describing the nonlocal conditions. Furthermore, a control steering the semilinear system from an initial state to a final state is exhibited.
{"title":"Controllability of time varying semilinear non-instantaneous impulsive systems with delay, and nonlocal conditions","authors":"Dalia Cabada, Katherine Garcia, Cristi D. Guevara, H. Leiva","doi":"10.24425/acs.2022.141715","DOIUrl":"https://doi.org/10.24425/acs.2022.141715","url":null,"abstract":"In this paper we prove the exact controllability of a time varying semilinear system considering non-instantaneous impulses, delay, and nonlocal conditions occurring simultaneously. It is done by using the Rothe’s fixed point theorem together with some sub-linear conditions on the nonlinear term, the impulsive functions, and the function describing the nonlocal conditions. Furthermore, a control steering the semilinear system from an initial state to a final state is exhibited.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"13 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87006517","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.2021.139735
Waldemar Kaczmarczyk
Small bucket models with many short fictitious micro-periods ensure high-quality schedules in multi-level systems, i.e., with multiple stages or dependent demand. In such models, setup times longer than a single period are, however, more likely. This paper presents new mixed-integer programming models for the proportional lot-sizing and scheduling problem (PLSP) with setup operations overlapping multiple periods with variable capacity. A new model is proposed that explicitly determines periods overlapped by each setup operation and the time spent on setup execution during each period. The model assumes that most periods have the same length; however, a few of them are shorter, and the time interval determined by two consecutive shorter periods is always longer than a single setup operation. The computational experiments show that the new model requires a significantly smaller computation effort than known models.
{"title":"Explicit modeling of multi-period setup times in proportional lot-sizing and scheduling problem with variable capacity","authors":"Waldemar Kaczmarczyk","doi":"10.24425/acs.2021.139735","DOIUrl":"https://doi.org/10.24425/acs.2021.139735","url":null,"abstract":"Small bucket models with many short fictitious micro-periods ensure high-quality schedules in multi-level systems, i.e., with multiple stages or dependent demand. In such models, setup times longer than a single period are, however, more likely. This paper presents new mixed-integer programming models for the proportional lot-sizing and scheduling problem (PLSP) with setup operations overlapping multiple periods with variable capacity. A new model is proposed that explicitly determines periods overlapped by each setup operation and the time spent on setup execution during each period. The model assumes that most periods have the same length; however, a few of them are shorter, and the time interval determined by two consecutive shorter periods is always longer than a single setup operation. The computational experiments show that the new model requires a significantly smaller computation effort than known models.","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":"73815110","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.2020.133499
Jun Wang, Xiaopu Shang, Xuehong Feng, Mengyang Sun
This paper aims to propose a new multi-attribute decision making (MADM) method in complicated and fuzzy decision-making environment. To express both decision makers (DMs’) quantitative and qualitative evaluation information comprehensively and consider their high hesitancy in giving their assessment values in MADM process, we combine q -rung dual hesitant fuzzy sets ( q -RDHFSs) with uncertain linguistic variables and develop a new tool, called the q -rung dual hesitant uncertain linguistic sets ( q -RDHULSs). First, the definition, operations and comparison method of q -RDHULSs are proposed. Second, given the interrelationship among multiple q -rung dual hesitant uncertain linguistic variables ( q -RDHULVs) we introduce some aggregation operators (AOs) to fuse q -rung dual hesitant uncertain linguistic ( q -RDHUL) information based on the Muirhead mean, i.e. the q -RDHUL Muirhead mean operator, the q RDHUL weighted Muirhead mean operator, the q -RDHUL dual Muirhead mean operator, and the q -RDHUL weighted dual Muirhead mean operator. To cope with MADM problems with q -RDHUL information, we propose a new method based on the proposed AOs. Afterwards, we apply the proposed method to an enterprise informatization level evaluation problem to verify its effectiveness. In addition, we also explain why our proposed method is more powerful and flexible than others.
{"title":"A novel multiple attribute decision making method based on q-rung dual hesitant uncertain linguistic sets and Muirhead mean","authors":"Jun Wang, Xiaopu Shang, Xuehong Feng, Mengyang Sun","doi":"10.24425/ACS.2020.133499","DOIUrl":"https://doi.org/10.24425/ACS.2020.133499","url":null,"abstract":"This paper aims to propose a new multi-attribute decision making (MADM) method in complicated and fuzzy decision-making environment. To express both decision makers (DMs’) quantitative and qualitative evaluation information comprehensively and consider their high hesitancy in giving their assessment values in MADM process, we combine q -rung dual hesitant fuzzy sets ( q -RDHFSs) with uncertain linguistic variables and develop a new tool, called the q -rung dual hesitant uncertain linguistic sets ( q -RDHULSs). First, the definition, operations and comparison method of q -RDHULSs are proposed. Second, given the interrelationship among multiple q -rung dual hesitant uncertain linguistic variables ( q -RDHULVs) we introduce some aggregation operators (AOs) to fuse q -rung dual hesitant uncertain linguistic ( q -RDHUL) information based on the Muirhead mean, i.e. the q -RDHUL Muirhead mean operator, the q RDHUL weighted Muirhead mean operator, the q -RDHUL dual Muirhead mean operator, and the q -RDHUL weighted dual Muirhead mean operator. To cope with MADM problems with q -RDHUL information, we propose a new method based on the proposed AOs. Afterwards, we apply the proposed method to an enterprise informatization level evaluation problem to verify its effectiveness. In addition, we also explain why our proposed method is more powerful and flexible than others.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"107 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77624074","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}
The current paradigm of modelling uncertainty in expert systems knowledge bases using Certainty Factors (CF) has been critically evaluated. A way to circumvent the awkwardness, non-intuitiveness and constraints encountered while using CF has been proposed. It is based on introducing Data Marks for askable conditions and Data Marks for conclusions of relational models, followed by choosing the best suited way to propagate those Data Marks into Data Marks of rule conclusions. This is done in a way orthogonal to the inference using Aristotelian Logic. Using Data Marks instead of Certainty Factors removes thus the intellectual discomfort caused by rejecting the notion of truth, falsehood and the Aristotelian law of excluded middle, as is done when using the CF methodology. There is also no need for changing the inference system software (expert system shell): the Data Marks approach can be implemented by simply modifying the knowledge base that should accommodate them. The methodology of using Data Marks to model uncertainty in knowledge bases has been illustrated by an example of SWOT analysis of a small electronic company. A short summary of SWOT analysis has been presented. The basic data used for SWOT analysis of the company are discussed. The rmes_EE SWOT knowledge base consisting of a rule base and model base have been presented and explained. The results of forward chaining for this knowledge base have been presented and critically evaluated.
{"title":"A new approach for modelling uncertainty in expert systems knowledge bases","authors":"A. Niederlinski","doi":"10.24425/119075","DOIUrl":"https://doi.org/10.24425/119075","url":null,"abstract":"The current paradigm of modelling uncertainty in expert systems knowledge bases using Certainty Factors (CF) has been critically evaluated. A way to circumvent the awkwardness, non-intuitiveness and constraints encountered while using CF has been proposed. It is based on introducing Data Marks for askable conditions and Data Marks for conclusions of relational models, followed by choosing the best suited way to propagate those Data Marks into Data Marks of rule conclusions. This is done in a way orthogonal to the inference using Aristotelian Logic. Using Data Marks instead of Certainty Factors removes thus the intellectual discomfort caused by rejecting the notion of truth, falsehood and the Aristotelian law of excluded middle, as is done when using the CF methodology. There is also no need for changing the inference system software (expert system shell): the Data Marks approach can be implemented by simply modifying the knowledge base that should accommodate them. The methodology of using Data Marks to model uncertainty in knowledge bases has been illustrated by an example of SWOT analysis of a small electronic company. A short summary of SWOT analysis has been presented. The basic data used for SWOT analysis of the company are discussed. The rmes_EE SWOT knowledge base consisting of a rule base and model base have been presented and explained. The results of forward chaining for this knowledge base have been presented and critically evaluated.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"39 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84742347","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.2021.136881
M. Niezabitowski, S. Popova, V. Zaitsev
Affine discrete-time control periodic systems are considered. The problem of global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has the Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic affine discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Examples of using the obtained results are presented.
{"title":"Sufficient conditions for uniform global asymptotic stabilization of affine discrete-time systems with periodic coefficients","authors":"M. Niezabitowski, S. Popova, V. Zaitsev","doi":"10.24425/acs.2021.136881","DOIUrl":"https://doi.org/10.24425/acs.2021.136881","url":null,"abstract":"Affine discrete-time control periodic systems are considered. The problem of global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has the Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic affine discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Examples of using the obtained results are presented.","PeriodicalId":48654,"journal":{"name":"Archives of Control Sciences","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78633612","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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