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Modelling of Complex Software Systems: a Reasoned Overview
"... This paper is devoted to the presentation of the key concepts on which a mathematical theory of complex (industrial) systems can be based. We especially show how this formal framework can capture the realness of modern information technologies. We also present some new modelling problems that are na ..."
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This paper is devoted to the presentation of the key concepts on which a mathematical theory of complex (industrial) systems can be based. We especially show how this formal framework can capture the realness of modern information technologies. We also present some new modelling problems that are naturally emerging in the specific context of complex software systems.
IDENTIFICATION OF SIMPLE ELEMENTS IN MAX ALGEBRA: APPLICATION TO SISO DISCRETE EVENT SYSTEMS MODELISATION
"... We propose to modelise the time behaviour of SISO discreteevent systems linear in Maxalgebra. The method is inspired from the conventional linear system theory: from the impulse response, the model is obtained by using a decomposition of the system into a sum of first order subsystems. From an ARM ..."
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We propose to modelise the time behaviour of SISO discreteevent systems linear in Maxalgebra. The method is inspired from the conventional linear system theory: from the impulse response, the model is obtained by using a decomposition of the system into a sum of first order subsystems. From an ARMA form, we compute the parameters of the model by using both results of residuation theory to minimise an error criterion and decomposition of periodic series. 1.
Keywords: DiscreteEvent Systems Feedback Control
"... For timed event graphs, linear models were obtained using MaxAlgebra. This paper presents a method to control such systems. After describing the optimal solution of a model tracking problem, we propose a feedback control structure in order to take into account a possible modeling error. We present ..."
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For timed event graphs, linear models were obtained using MaxAlgebra. This paper presents a method to control such systems. After describing the optimal solution of a model tracking problem, we propose a feedback control structure in order to take into account a possible modeling error. We present its construction, its main properties and an algorithm for its practical implementation. An illustrative example is provided. 1
Symmetry, Integrability and Geometry: Methods and Applications Ultradiscrete sineGordon Equation over Symmetrized MaxPlus Algebra, and Noncommutative Discrete and Ultradiscrete sineGordon Equations
"... Abstract. Ultradiscretization with negative values is a longstanding problem and several attempts have been made to solve it. Among others, we focus on the symmetrized maxplus algebra, with which we ultradiscretize the discrete sineGordon equation. Another ultradiscretization of the discrete sine ..."
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Abstract. Ultradiscretization with negative values is a longstanding problem and several attempts have been made to solve it. Among others, we focus on the symmetrized maxplus algebra, with which we ultradiscretize the discrete sineGordon equation. Another ultradiscretization of the discrete sineGordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sineGordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sineGordon equation and its 1soliton and 2soliton solutions, using the symmetrized maxplus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sineGordon equations. Key words: ultradiscrete sineGordon equation; symmetrized maxplus algebra; noncommutative discrete sineGordon equation; noncommutative ultradiscrete sineGordon equation 2010 Mathematics Subject Classification: 37K10; 39A12 1
Author manuscript, published in "ECC'97, Bruxelles: Belgium (1997)" IDENTIFICATION OF SIMPLE ELEMENTS IN MAX ALGEBRA: APPLICATION TO SISO DISCRETE EVENT SYSTEMS MODELISATION
, 2013
"... We propose to modelise the time behaviour of SISO discreteevent systems linear in Maxalgebra. The method is inspired from the conventional linear system theory: from the impulse response, the model is obtained by using a decomposition of the system into a sum of first order subsystems. From an ARM ..."
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We propose to modelise the time behaviour of SISO discreteevent systems linear in Maxalgebra. The method is inspired from the conventional linear system theory: from the impulse response, the model is obtained by using a decomposition of the system into a sum of first order subsystems. From an ARMA form, we compute the parameters of the model by using both results of residuation theory to minimise an error criterion and decomposition of periodic series. 1.
Author manuscript, published in "ECC'97, Bruxelles: Belgium (1997)" A Feedback Control in MaxAlgebra
, 2013
"... For timed event graphs, linear models were obtained using MaxAlgebra. This paper presents a method to control such systems. After describing the optimal solution of a model tracking problem, we propose a feedback control structure in order to take into account a possible modeling error. We present ..."
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For timed event graphs, linear models were obtained using MaxAlgebra. This paper presents a method to control such systems. After describing the optimal solution of a model tracking problem, we propose a feedback control structure in order to take into account a possible modeling error. We present its construction, its main properties and an algorithm for its practical implementation. An illustrative example is provided. 1
Ultradiscrete sineGordon Equation over Symmetrized MaxPlus Algebra, and Noncommutative Discrete and Ultradiscrete sineGordon Equations
"... Abstract. Ultradiscretization with negative values is a longstanding problem and several attempts have been made to solve it. Among others, we focus on the symmetrized maxplus algebra, with which we ultradiscretize the discrete sineGordon equation. Another ultradiscretization of the discrete sin ..."
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Abstract. Ultradiscretization with negative values is a longstanding problem and several attempts have been made to solve it. Among others, we focus on the symmetrized maxplus algebra, with which we ultradiscretize the discrete sineGordon equation. Another ultradiscretization of the discrete sineGordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sineGordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sineGordon equation and its 1soliton and 2soliton solutions, using the symmetrized maxplus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sineGordon equations. Key words: ultradiscrete sineGordon equation; symmetrized maxplus algebra; noncommutative discrete sineGordon equation; noncommutative ultradiscrete sineGordon equation 2010 Mathematics Subject Classification: 37K10; 39A12 1