Abstract Preferential information may be visualized in many different ways, and this constitutes an important issue in the principal-agent decision-making context, e.g., in representative negotiations. In the INSPIRE negotiation support system, the principal’s preferences are visualized by circles with different radii. Agents evaluate the principal’s preferences in such a manner that they digitize these preferences using numbers directly proportional to the size of the circles, drawn by the principal. The manner, in which an agent understands the concept of the circle size is unknown. The main goal of this paper is to propose such an image of principal’s preferences, which is independent of an individual agent’s evaluation. Individual negotiators may differ in their understanding of this concept. This means that the notion of “circle size” is a linguistic variable that may be described by a fuzzy set. The empirical studies referred to show that the size of the circle is a value between the radius and the area of this circle. In this paper, the principal’s preferences are defined as a fuzzy preorder between fuzzy “circle sizes”. We distinguish here two kinds of the INSPIRE method. All considerations are illustrated by means of a short case study based on INSPIRE data.
{"title":"A fuzzy ranking of negotiation packages for the INSPIRE negotiation support system","authors":"Krzysztof Piasecki","doi":"10.2478/candc-2021-0005","DOIUrl":"https://doi.org/10.2478/candc-2021-0005","url":null,"abstract":"Abstract Preferential information may be visualized in many different ways, and this constitutes an important issue in the principal-agent decision-making context, e.g., in representative negotiations. In the INSPIRE negotiation support system, the principal’s preferences are visualized by circles with different radii. Agents evaluate the principal’s preferences in such a manner that they digitize these preferences using numbers directly proportional to the size of the circles, drawn by the principal. The manner, in which an agent understands the concept of the circle size is unknown. The main goal of this paper is to propose such an image of principal’s preferences, which is independent of an individual agent’s evaluation. Individual negotiators may differ in their understanding of this concept. This means that the notion of “circle size” is a linguistic variable that may be described by a fuzzy set. The empirical studies referred to show that the size of the circle is a value between the radius and the area of this circle. In this paper, the principal’s preferences are defined as a fuzzy preorder between fuzzy “circle sizes”. We distinguish here two kinds of the INSPIRE method. All considerations are illustrated by means of a short case study based on INSPIRE data.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"69 - 82"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46670999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Richard Krug, G. Leugering, Alexander Martin, Martin Schmidt, Dieter Weninger
Abstract In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.
{"title":"Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions","authors":"Richard Krug, G. Leugering, Alexander Martin, Martin Schmidt, Dieter Weninger","doi":"10.1137/20m138329x","DOIUrl":"https://doi.org/10.1137/20m138329x","url":null,"abstract":"Abstract In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"427 - 455"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41660143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.1007/978-3-319-31274-3_6
J. Kaur, Amit Kumar
{"title":"Unique fuzzy optimal value of fully fuzzy linear programming problems","authors":"J. Kaur, Amit Kumar","doi":"10.1007/978-3-319-31274-3_6","DOIUrl":"https://doi.org/10.1007/978-3-319-31274-3_6","url":null,"abstract":"","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"GE-19 2","pages":"497-508"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/978-3-319-31274-3_6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51014436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-03-08DOI: 10.1108/03321641111101131
T. Kaczorek
Purpose – The purpose of this paper is to formulate and solve the pointwise completeness and pointwise degeneracy of standard and positive 2D Fornasini‐Marchesini and 2D Roesser models.Design/methodology/approach – A procedure is proposed for investigation of the pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini‐Marchesini and Roesser models.Findings – Necessary and sufficient conditions for pointwise completeness and pointwise degeneracy of standard and positive Fornasini‐Marchesini and Roesser models are established.Originality/value – The paper proposes a method for investigation of the pointwise completeness and pointwise degeneracy of the standard and positive Fornasini‐Marchesini and Roesser models.
{"title":"Pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini-Marchesini models with state-feedbacks","authors":"T. Kaczorek","doi":"10.1108/03321641111101131","DOIUrl":"https://doi.org/10.1108/03321641111101131","url":null,"abstract":"Purpose – The purpose of this paper is to formulate and solve the pointwise completeness and pointwise degeneracy of standard and positive 2D Fornasini‐Marchesini and 2D Roesser models.Design/methodology/approach – A procedure is proposed for investigation of the pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini‐Marchesini and Roesser models.Findings – Necessary and sufficient conditions for pointwise completeness and pointwise degeneracy of standard and positive Fornasini‐Marchesini and Roesser models are established.Originality/value – The paper proposes a method for investigation of the pointwise completeness and pointwise degeneracy of the standard and positive Fornasini‐Marchesini and Roesser models.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"40 1","pages":"39-58"},"PeriodicalIF":0.0,"publicationDate":"2011-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1108/03321641111101131","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62067711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-01-01DOI: 10.2478/V10170-010-0006-7
J. Duda
The paper presents a method of determining of the Lyapunov quadratic functional for linear time-invariant system with two delays both retarded and neutral type. The Lyapunov functional is constructed for a given its time derivative which is calculated on the trajectory of the system with two delays both retarded and neutral type. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
{"title":"Lyapunov functional for a linear system with two delays","authors":"J. Duda","doi":"10.2478/V10170-010-0006-7","DOIUrl":"https://doi.org/10.2478/V10170-010-0006-7","url":null,"abstract":"The paper presents a method of determining of the Lyapunov quadratic functional for linear time-invariant system with two delays both retarded and neutral type. The Lyapunov functional is constructed for a given its time derivative which is calculated on the trajectory of the system with two delays both retarded and neutral type. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"39 1","pages":"797-809"},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2478/V10170-010-0006-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68990400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-06-01DOI: 10.2478/V10175-010-0116-1
H. Górecki
The relation between extremal values of the error and the coefficients of its differential equations is one of the central problems of control systems in chemical industry, becouse extremal values of the error sometimes cause serious damages to the environment or to the system itself. Analytical formulae for the determination of these values are known only for the second-order systems. In this paper a method which permits to determine extremal values of the error in higher-order systems is proposed.
{"title":"A new method for analytic determination of extremum of the transients in linear systems","authors":"H. Górecki","doi":"10.2478/V10175-010-0116-1","DOIUrl":"https://doi.org/10.2478/V10175-010-0116-1","url":null,"abstract":"The relation between extremal values of the error and the coefficients of its differential equations is one of the central problems of control systems in chemical industry, becouse extremal values of the error sometimes cause serious damages to the environment or to the system itself. Analytical formulae for the determination of these values are known only for the second-order systems. In this paper a method which permits to determine extremal values of the error in higher-order systems is proposed.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"33 1","pages":"275-295"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69039399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In two previous works we improved some earlier results of Imanuvilov, Li and Zhang, and of Zuazua on the boundary exact controllability of one-dimensional semilinear wave equations by weakening the growth assumptions on the nonlinearity. Our growth assumption is in a sense optimal. Here we adapt our method for the case of one-sided control actions. This also enables us to obtain rather general internal controllability results.
{"title":"Controllability of semilinear wave equations with infinitely iterated logarithms","authors":"P. Cannarsa, V. Komornik, P. Loreti","doi":"10.3934/DCDS.2002.8.747","DOIUrl":"https://doi.org/10.3934/DCDS.2002.8.747","url":null,"abstract":"In two previous works we improved some earlier results of Imanuvilov, Li \u0000and Zhang, and of Zuazua on the boundary exact controllability of one-dimensional \u0000semilinear wave equations by weakening the growth assumptions on the nonlinearity. \u0000Our growth assumption is in a sense optimal. Here we adapt our method for the case \u0000of one-sided control actions. This also enables us to obtain rather general internal \u0000controllability results.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"28 1","pages":"449-461"},"PeriodicalIF":0.0,"publicationDate":"2002-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3934/DCDS.2002.8.747","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70222000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2000-09-01DOI: 10.1016/S1474-6670(17)36319-X
T. Kaczorek
{"title":"Reachability and controllability of 2D positive linear systems with state feedbacks","authors":"T. Kaczorek","doi":"10.1016/S1474-6670(17)36319-X","DOIUrl":"https://doi.org/10.1016/S1474-6670(17)36319-X","url":null,"abstract":"","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"29 1","pages":"141-151"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1474-6670(17)36319-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56569946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A family of parameter dependent optimal control poblems for nonlinear ODEs is considered. The problems are subject to pointwise control and state inequality type constraints. It is assumed that, at the reference value of the parameter the reference optimal solution exists and is regular. Regularity conditions are formulated under which the original problems are locally equivalent to some problems subject to equality type constraints only. The classical implicit function theorem is applied to these new problems to investigate Frechet differentiability of the solutions with respect to the parameter. A numerical example is provided.
{"title":"Sensitivity analysis for state constrained optimal control problems","authors":"K. Malanowski, Helmut Maurer","doi":"10.3934/DCDS.1998.4.241","DOIUrl":"https://doi.org/10.3934/DCDS.1998.4.241","url":null,"abstract":"A family of parameter dependent optimal control poblems for nonlinear \u0000ODEs is considered. The problems are subject to pointwise control and state inequality type constraints. It is assumed that, at the reference value of the parameter \u0000the reference optimal solution exists and is regular. Regularity conditions are formulated under which the original problems are locally equivalent to some problems \u0000subject to equality type constraints only. The classical implicit function theorem is \u0000applied to these new problems to investigate Frechet differentiability of the solutions \u0000with respect to the parameter. A numerical example is provided.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"40 1","pages":"1043-1058"},"PeriodicalIF":0.0,"publicationDate":"1998-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3934/DCDS.1998.4.241","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1993-01-01DOI: 10.1007/978-3-662-12629-5_70
K. Szajowski, W. L. Koning
{"title":"Discrete-time Markovian jump linear systems","authors":"K. Szajowski, W. L. Koning","doi":"10.1007/978-3-662-12629-5_70","DOIUrl":"https://doi.org/10.1007/978-3-662-12629-5_70","url":null,"abstract":"","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"27 1","pages":"63-80"},"PeriodicalIF":0.0,"publicationDate":"1993-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51327913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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