Pub Date : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.155
M. Merca
In this paper, the author considered two specializations of the identity q-Chu Vandermonde and derived two recurrence relations for the number of partitions of n into m parts with the smallest part greater than or equal to k and the minimal difference d.
{"title":"ON THE NUMBER OF PARTITIONS INTO PARTS WITH THE MINIMAL PART k AND THE MINIMAL DIFFERENCE d","authors":"M. Merca","doi":"10.56082/annalsarscimath.2020.1-2.155","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.155","url":null,"abstract":"In this paper, the author considered two specializations of the identity q-Chu Vandermonde and derived two recurrence relations for the number of partitions of n into m parts with the smallest part greater than or equal to k and the minimal difference d.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76533076","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.405
A. M. de Oliveira, O. Costa
In this chapter we discuss the H2 control for Markov jump linear systems in a context of partial observation of both the Markov chain and the state variable. The controller is static and depends on an observed variable that provides the only information of the Markov variable in a context of hidden Markov chains. We propose a new design condition in terms of linear matrix inequalities considering rank constraints in suitable system matrices that are easily fulfilled. Next we investigate the case in which the detector provides perfect estimations of the Markov chain and all the states are available to the controller. Finally we compare this result with the so-called two-step procedure for hidden Markov jump linear systems in an academic example of a system subject to faults.
{"title":"ON THE H2 STATIC OUTPUT FEEDBACK CONTROL FOR HIDDEN MARKOV JUMP LINEAR SYSTEMS","authors":"A. M. de Oliveira, O. Costa","doi":"10.56082/annalsarscimath.2020.1-2.405","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.405","url":null,"abstract":"In this chapter we discuss the H2 control for Markov jump linear systems in a context of partial observation of both the Markov chain and the state variable. The controller is static and depends on an observed variable that provides the only information of the Markov variable in a context of hidden Markov chains. We propose a new design condition in terms of linear matrix inequalities considering rank constraints in suitable system matrices that are easily fulfilled. Next we investigate the case in which the detector provides perfect estimations of the Markov chain and all the states are available to the controller. Finally we compare this result with the so-called two-step procedure for hidden Markov jump linear systems in an academic example of a system subject to faults.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79484146","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.564
M. A. Rami
This paper provides a treatment for the mode-dependent static output-feedback control problem of linear systems subject to random Markovian jumps in its parameters. For this kind of systems, we consider the mean-square stability and we develop a numerical method to find static output-feedback stabilizing control. We show how one can handle the uncertainties that can affect the transition probability matrix. The robust static output-feedback stabilization problem (against unkown or uncertain probability rates) is formulated in terms of the minimization of a scalar product of definite positive matrices under convex constraint (LMIs). Such problem can be solved via a cone complementarity algorithm.
{"title":"STATIC OUTPUT-FEEDBACK STABILIZATION OF MARKOVIAN JUMP SYSTEMS WITH UNCERTAIN PROBABILITY RATES","authors":"M. A. Rami","doi":"10.56082/annalsarscimath.2020.1-2.564","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.564","url":null,"abstract":"This paper provides a treatment for the mode-dependent static output-feedback control problem of linear systems subject to random Markovian jumps in its parameters. For this kind of systems, we consider the mean-square stability and we develop a numerical method to find static output-feedback stabilizing control. We show how one can handle the uncertainties that can affect the transition probability matrix. The robust static output-feedback stabilization problem (against unkown or uncertain probability rates) is formulated in terms of the minimization of a scalar product of definite positive matrices under convex constraint (LMIs). Such problem can be solved via a cone complementarity algorithm.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87133388","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.256
I. Popa, T. Ceausu, L. Biris, Tongxing Li, A. Zada
This paper presents a new approach to formulating exponential behaviors like stability/instability for the linear time-varying systems and for the adjoint one. The classical concept of uniform exponential stability is generalized. Using this generalized concepts, some results extending existing uniform exponential stability conditions for linear time-varying systems are derived. As special cases for these results, some conditions are derived for the adjoint system. A characterization of the generalized concepts in terms of Lyapunov sequences is also given. Also, an example is included to further illustrate the connection with the classical concept of uniform exponential stability.
{"title":"GENERALIZED EXPONENTIALLY STABLE LINEAR TIME-VARYING DISCRETE BEHAVIORS","authors":"I. Popa, T. Ceausu, L. Biris, Tongxing Li, A. Zada","doi":"10.56082/annalsarscimath.2020.1-2.256","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.256","url":null,"abstract":"This paper presents a new approach to formulating exponential behaviors like stability/instability for the linear time-varying systems and for the adjoint one. The classical concept of uniform exponential stability is generalized. Using this generalized concepts, some results extending existing uniform exponential stability conditions for linear time-varying systems are derived. As special cases for these results, some conditions are derived for the adjoint system. A characterization of the generalized concepts in terms of Lyapunov sequences is also given. Also, an example is included to further illustrate the connection with the classical concept of uniform exponential stability.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80755368","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.164
Bozhidar Angelov Stanchev, Hristo Paraskevov
"In this paper we present an edge swapping approach for incorporating line segments into triangulation. If the initial triangulation is Delaunay, the algorithm tends to produce optimal Constrained Delaunay triangulation by improving the triangles’ aspect ratios from the local area being constrained. There are two types of methods for constructing Constrained Delaunay Triangulation: straight-forward ones which take both points and line segments as source data and produce constrained triangulation from them at once; and post-processing ones which take an already constructed triangulation and incorporate line segments into it. While most of the existing post-processing approaches clear the triangle’s edges intersected by the line segment being incorporated and fill the opened hole (cavity) by re-triangulating it, the only processing that our algorithm does is to change the triangulation connectivity and to improve the triangles’ aspect ratios through edge swapping. Hereof, it is less expensive in terms of both operating and memory costs. The motivation behind our approach is that most of the existing straight-forward triangulators are too slow and not stable enough. The idea is to use pure Delaunay triangulator to produce an initial Delaunay triangulation and later on to constrain it to the line segments (in other words, to split the processing into two steps, each of which is stable enough and the combination of them works much faster). The algorithm also minimizes the number of the newly introduced triangulation points - new points are added only if any of the line segment’s endpoints does not match an existing triangulation point."
{"title":"CONSTRAINING TRIANGULATION TO LINE SEGMENTS: A FAST METHOD FOR CONSTRUCTING CONSTRAINED DELAUNAY TRIANGULATION","authors":"Bozhidar Angelov Stanchev, Hristo Paraskevov","doi":"10.56082/annalsarscimath.2020.1-2.164","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.164","url":null,"abstract":"\"In this paper we present an edge swapping approach for incorporating line segments into triangulation. If the initial triangulation is Delaunay, the algorithm tends to produce optimal Constrained Delaunay triangulation by improving the triangles’ aspect ratios from the local area being constrained. There are two types of methods for constructing Constrained Delaunay Triangulation: straight-forward ones which take both points and line segments as source data and produce constrained triangulation from them at once; and post-processing ones which take an already constructed triangulation and incorporate line segments into it. While most of the existing post-processing approaches clear the triangle’s edges intersected by the line segment being incorporated and fill the opened hole (cavity) by re-triangulating it, the only processing that our algorithm does is to change the triangulation connectivity and to improve the triangles’ aspect ratios through edge swapping. Hereof, it is less expensive in terms of both operating and memory costs. The motivation behind our approach is that most of the existing straight-forward triangulators are too slow and not stable enough. The idea is to use pure Delaunay triangulator to produce an initial Delaunay triangulation and later on to constrain it to the line segments (in other words, to split the processing into two steps, each of which is stable enough and the combination of them works much faster). The algorithm also minimizes the number of the newly introduced triangulation points - new points are added only if any of the line segment’s endpoints does not match an existing triangulation point.\"","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89243366","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.51
A. Cernea
We consider a fractional differential inclusion involving CaputoFabrizio fractional derivative and we obtain a sufficient condition for h-local controllability along a reference trajectory. To derive this result we use convex linearizations of the fractional differential inclusion. More precisely, we show that the fractional differential inclusion is hlocally controlable around a solution z if a certain linearized inclusion is λ-locally controlable around the null solution for every λ ∈ ∂h(z(T)), where ∂h denotes Clarke’s generalized Jacobian of the locally Lipschitz function h.
{"title":"ON CONTROLLABILITY FOR A FRACTIONAL DIFFERENTIAL INCLUSION OF CAPUTO-FABRIZIO TYPE","authors":"A. Cernea","doi":"10.56082/annalsarscimath.2020.1-2.51","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.51","url":null,"abstract":"We consider a fractional differential inclusion involving CaputoFabrizio fractional derivative and we obtain a sufficient condition for h-local controllability along a reference trajectory. To derive this result we use convex linearizations of the fractional differential inclusion. More precisely, we show that the fractional differential inclusion is hlocally controlable around a solution z if a certain linearized inclusion is λ-locally controlable around the null solution for every λ ∈ ∂h(z(T)), where ∂h denotes Clarke’s generalized Jacobian of the locally Lipschitz function h.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79277645","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.7
T. Morozan, V. Rǎsvan, D. Tiba
This volume is dedicated to the 70th anniversary of Vasile Dr˘agan, an internationally recognized researcher in the area of system and control theory. The impressive scientific results of Vasile Dragan are the output of a life-time sustained work and his special talent for Mathematics. This is a story of ”A Beautiful Mind”. On this occasion, his collaborators and his colleagues wish him long life in good health and happiness, and more achievements in the field of science
这一卷是献给国际公认的系统和控制理论领域的研究员瓦西里·× ×根(Vasile Dr × agan) 70周年的。Vasile Dragan令人印象深刻的科学成果是他一生持续工作和他在数学方面的特殊才能的产物。这是一个关于《美丽心灵》的故事。借此机会，他的合作者和同事们祝愿他身体健康，幸福长寿，在科学领域取得更多成就
{"title":"VASILE DRĂGAN AT HIS 70TH BIRTHDAY","authors":"T. Morozan, V. Rǎsvan, D. Tiba","doi":"10.56082/annalsarscimath.2020.1-2.7","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.7","url":null,"abstract":"This volume is dedicated to the 70th anniversary of Vasile Dr˘agan, an internationally recognized researcher in the area of system and control theory. The impressive scientific results of Vasile Dragan are the output of a life-time sustained work and his special talent for Mathematics. This is a story of ”A Beautiful Mind”. On this occasion, his collaborators and his colleagues wish him long life in good health and happiness, and more achievements in the field of science","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73836206","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.522
S. Aberkane
In this paper we obtain existence conditions for the solution of a class of generalized Riccati equations arising in finite horizon linear quadratic (LQ) mean-field games.
本文给出了有限视界线性二次平均场对策中一类广义Riccati方程解的存在性条件。
{"title":"ON THE EXISTENCE OF THE SOLUTION OF RICCATI EQUATIONS ARISING IN LINEAR QUADRATIC MEAN FIELD DYNAMIC GAMES","authors":"S. Aberkane","doi":"10.56082/annalsarscimath.2020.1-2.522","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.522","url":null,"abstract":"In this paper we obtain existence conditions for the solution of a class of generalized Riccati equations arising in finite horizon linear quadratic (LQ) mean-field games.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80513726","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.425
A. Stoica, I. Yaesh
The design of static output feedback controllers in an anisotropic norm setup is considered. The aim is to determine a stabilizing static output feedback for a given four block system such that the resulting closed loop system has the a-anisotropic norm less than a given γ > 0. The solvability conditions are expressed in terms of the solution of a rank minimization problem with linear matrix inequalities constraints. Based on the specific form of these constraints it is shown that a solution of this problem may be obtained solving a semidefinite programming problem.
{"title":"STATIC OUTPUT FEEDBACK DESIGN IN AN ANISOTROPIC NORM SETUP","authors":"A. Stoica, I. Yaesh","doi":"10.56082/annalsarscimath.2020.1-2.425","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.425","url":null,"abstract":"The design of static output feedback controllers in an anisotropic norm setup is considered. The aim is to determine a stabilizing static output feedback for a given four block system such that the resulting closed loop system has the a-anisotropic norm less than a given γ > 0. The solvability conditions are expressed in terms of the solution of a rank minimization problem with linear matrix inequalities constraints. Based on the specific form of these constraints it is shown that a solution of this problem may be obtained solving a semidefinite programming problem.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77515945","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 : 2020-01-01DOI: 10.56082/annalsarscimath.2020.1-2.501
Fortià V. Vergés, M. Fragoso
This paper makes a further foray on the study of the filtering problem for the class of Markov jump linear systems (MJLSs) with partial observations of the Markov parameter (the operation mode). We derive a stationary filter for the best linear mean square filter (BLMSF) devised in a recent paper by the authors. It amounts here to obtain the convergence of the error covariance matrix of the best linear mean square filter to a stationary value under some suitable assumptions which includes ergodicity of the Markov chain. The advantage of this scheme is that it is easier to implement since the filter gain computation can be performed offline, leading to a linear time-invariant filter.
{"title":"STATIONARY LINEAR MEAN SQUARE FILTER FOR THE OPERATION MODE OF CONTINUOUS-TIME MARKOVIAN JUMP LINEAR SYSTEMS","authors":"Fortià V. Vergés, M. Fragoso","doi":"10.56082/annalsarscimath.2020.1-2.501","DOIUrl":"https://doi.org/10.56082/annalsarscimath.2020.1-2.501","url":null,"abstract":"This paper makes a further foray on the study of the filtering problem for the class of Markov jump linear systems (MJLSs) with partial observations of the Markov parameter (the operation mode). We derive a stationary filter for the best linear mean square filter (BLMSF) devised in a recent paper by the authors. It amounts here to obtain the convergence of the error covariance matrix of the best linear mean square filter to a stationary value under some suitable assumptions which includes ergodicity of the Markov chain. The advantage of this scheme is that it is easier to implement since the filter gain computation can be performed offline, leading to a linear time-invariant filter.","PeriodicalId":38807,"journal":{"name":"Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86878231","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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