165 results
Search Results
152. Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs
- Author
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Mehmet Emir Koksal and OMÜ
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Differential equations ,feedback circuits ,0209 industrial biotechnology ,Pure mathematics ,Differential equation ,General Mathematics ,Robust control ,34h99 ,Analogue control ,02 engineering and technology ,Feedback control systems ,Series and parallel circuits ,93c05 ,93a30 ,020901 industrial engineering & automation ,QA1-939 ,0202 electrical engineering, electronic engineering, information engineering ,Decomposition (computer science) ,feedback control systems ,Feedback circuits ,Time complexity ,Commutative property ,Mathematics ,Discrete mathematics ,Equivalent circuits ,differential equations ,Order (ring theory) ,93c99 ,93b35 ,analogue control ,93c15 ,Equivalent circuit ,020201 artificial intelligence & image processing ,equivalent circuits ,robust control - Abstract
emir/0000-0001-7220-0042 WOS: 000386878300001 Necessary and sufficiently conditions are derived for the decomposition of a second order linear time-varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself. Scientific and Technological Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [115E952] This paper has been supported by the Scientific and Technological Research Council of Turkey under the project no. 115E952.
- Published
- 2016
153. Global stability analysis and control of leptospirosis
- Author
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Mirirai Mukamuri, Daniel Oluwole Makinde, and Kazeem Oare Okosun
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0301 basic medicine ,Operations research ,General Mathematics ,Control (management) ,Stability (learning theory) ,stability analysis ,92b05 ,medicine.disease ,Optimal control ,Leptospirosis ,93c15 ,optimal control ,93a30 ,03 medical and health sciences ,030104 developmental biology ,QA1-939 ,medicine ,leptospirosis ,cost-effectiveness analaysis ,anova ,Mathematics - Abstract
The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.
- Published
- 2016
154. Hybrid Modelling in Biology: a Classification Review
- Author
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Vitaly Volpert, Angélique Stéphanou, Dynamique Cellulaire et Tissulaire- Interdisciplinarité, Modèles & Microscopies (TIMC-IMAG-DyCTiM), Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525 (TIMC-IMAG), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), Dynamiques Cellulaire et Tissulaire - Interdisciplinarité, Modélisation & Microscopie (TIMC-IMAG-DyCTiM2), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), and Institut Camille Jordan (ICJ)
- Subjects
Mathematics Subject Classification: 35Q92 ,0301 basic medicine ,68R0 ,Theoretical computer science ,Systems biology ,Complex system ,hybrid model ,93C55 ,Context (language use) ,92B05 ,03 medical and health sciences ,92C50 ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,system biology ,Applied Mathematics ,Rotation formalisms in three dimensions ,discrete–continuous ,Coupling (physics) ,93A30 ,030104 developmental biology ,multiscale ,Homogeneous ,Modeling and Simulation ,Hybrid system ,92C42 ,Hybrid model ,and phrases: complex system - Abstract
International audience; This paper presents a general review on hybrid modelling which is about to become ubiquitous in biological and medical modelling. Hybrid modelling is classically defined as the coupling of a continuous approach with a discrete one, in order to model a complex phenomenon that cannot be described in a standard homogeneous way mainly due to its inherent multiscale nature. In fact, hybrid modelling can be more than that since any types of coupled formalisms qualify as being hybrid. This review first presents the evolution and current context of this modelling approach. It then proposes a classification of the models through three different types that relate to the nature and level of coupling of the formalisms used.
- Published
- 2015
155. An inner product space on irreducible and synchronizable probabilistic finite state automata
- Author
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Adenis, Patrick, Wen, Yicheng, and Ray, Asok
- Published
- 2012
- Full Text
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156. Partial realization theory and system identification redux
- Author
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Anders Lindquist
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Computer science ,System identification ,Context (language use) ,Kalman filter ,Algebra ,Matrix (mathematics) ,93A30 ,Optimization and Control (math.OC) ,FOS: Mathematics ,Riccati equation ,Control (linguistics) ,Mathematics - Optimization and Control ,Realization (systems) ,Interpolation - Abstract
Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows us to show that the nonstandard matrix Riccati equation is universal in the sense that it can be used to solve more general analytic interpolation problems by only changing certain parameters. Such interpolation problems are ubiquitous in systems and control. In this context we also discuss a question posed by R.E. Kalman in beginning of the 1970s.
- Published
- 2017
157. Dynamic Social Balance and Convergent Appraisals via Homophily and Influence Mechanisms
- Author
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Pedro Cisneros-Velarde, Noah E. Friedkin, Ge Chen, Wenjun Mei, and Francesco Bullo
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FOS: Computer and information sciences ,0209 industrial biotechnology ,Dynamical systems theory ,Computer science ,91D30 ,02 engineering and technology ,Structural balance ,Network topology ,Homophily ,Mathematical Sciences ,Homophily/Influence mechanisms ,020901 industrial engineering & automation ,Engineering ,Information and Computing Sciences ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,Electrical and Electronic Engineering ,Equivalence (measure theory) ,Equilibrium point ,Social and Information Networks (cs.SI) ,Nonlinear network dynamics ,Multi-agent system ,020208 electrical & electronic engineering ,Multi-agent systems ,91D30, 37N99, 93A30 ,Computer Science - Social and Information Networks ,Computer Science::Social and Information Networks ,Computer Science::Computers and Society ,93A30 ,Industrial Engineering & Automation ,Control and Systems Engineering ,Bounded function ,37N99 ,Mathematical economics ,cs.SI - Abstract
Social balance theory describes allowable and forbidden configurations of the topologies of signed directed social appraisal networks. In this paper, we propose two discrete-time dynamical systems that explain how an appraisal network \textcolor{blue}{converges to} social balance from an initially unbalanced configuration. These two models are based on two different socio-psychological mechanisms respectively: the homophily mechanism and the influence mechanism. Our main theoretical contribution is a comprehensive analysis for both models in three steps. First, we establish the well-posedness and bounded evolution of the interpersonal appraisals. Second, we fully characterize the set of equilibrium points; for both models, each equilibrium network is composed by an arbitrary number of complete subgraphs satisfying structural balance. Third, we establish the equivalence among three distinct properties: non-vanishing appraisals, convergence to all-to-all appraisal networks, and finite-time achievement of social balance. In addition to theoretical analysis, Monte Carlo validations illustrates how the non-vanishing appraisal condition holds for generic initial conditions in both models. Moreover, numerical comparison between the two models indicate that the homophily-based model might be a more universal explanation for the formation of social balance. Finally, adopting the homophily-based model, we present numerical results on the mediation and globalization of local conflicts, the competition for allies, and the asymptotic formation of a single versus two factions.
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- 2017
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- View/download PDF
158. Dynamic models of appraisal networks explaining collective learning
- Author
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Kyle Lewis, Noah E. Friedkin, Wenjun Mei, and Francesco Bullo
- Subjects
FOS: Computer and information sciences ,0209 industrial biotechnology ,J.4 ,Computer science ,02 engineering and technology ,Task (project management) ,multiagent systems ,020901 industrial engineering & automation ,Replicator equation ,multi-agent systems ,Mathematics - Optimization and Control ,Sequence ,I.2.11 ,Management science ,transactive memory systems ,Applied Mathematics ,91D30, 37N99, 93A30 ,05 social sciences ,transactive memory system ,collective learning ,Computer Science - Social and Information Networks ,Collaborative learning ,influence network ,cs.SY ,Computer Science Applications ,93A30 ,Mental Health ,Dynamic models ,cs.SI ,Multiagent Systems (cs.MA) ,Cognitive psychology ,Mathematical sociology ,Process (engineering) ,evolutionary games ,91D30 ,Bioengineering ,Systems and Control (eess.SY) ,Interpersonal communication ,replicator dynamics ,appraisal network ,Clinical Research ,0502 economics and business ,Transactive memory ,FOS: Electrical engineering, electronic engineering, information engineering ,FOS: Mathematics ,Computer Science - Multiagent Systems ,Electrical and Electronic Engineering ,Social and Information Networks (cs.SI) ,math.OC ,Appraisal networks ,Mechanical Engineering ,Industrial Engineering & Automation ,Optimization and Control (math.OC) ,Control and Systems Engineering ,37N99 ,Computer Science - Systems and Control ,influence networks ,050203 business & management ,cs.MA - Abstract
This paper proposes models of learning process in teams of individuals who collectively execute a sequence of tasks and whose actions are determined by individual skill levels and networks of interpersonal appraisals and influence. The closely-related proposed models have increasing complexity, starting with a centralized manager-based assignment and learning model, and finishing with a social model of interpersonal appraisal, assignments, learning, and influences. We show how rational optimal behavior arises along the task sequence for each model, and discuss conditions of suboptimality. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science., Comment: A preliminary version has been accepted by the 53rd IEEE Conference on Decision and Control. The journal version has been submitted to IEEE Transactions on Automatic Control
- Published
- 2016
159. On local and global sigma-pi neural networks a common link
- Author
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Lenze, Burkhard
- Published
- 1994
- Full Text
- View/download PDF
160. Dynamic Models of Appraisal Networks Explaining Collective Learning
- Author
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Mei, W, Friedkin, NE, Lewis, K, Bullo, F, and IEEE
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I.2.11 ,math.OC ,J.4 ,transactive memory system ,evolutionary games ,collective learning ,91D30 ,Bioengineering ,influence network ,cs.SY ,replicator dynamics ,appraisal network ,Mental Health ,93A30 ,Clinical Research ,37N99 ,multi-agent systems ,cs.SI ,cs.MA - Abstract
This paper proposes models of learning process in teams of individuals who collectively execute a sequence of tasks and whose actions are determined by individual skill levels and networks of interpersonal appraisals and influence. The closely-related proposed models have increasing complexity, starting with a centralized manager-based assignment and learning model, and finishing with a social model of interpersonal appraisal, assignments, learning, and influences. We show how rational optimal behavior arises along the task sequence for each model, and discuss conditions of suboptimality. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science.
- Published
- 2016
161. Role of environmental persistence in pathogen transmission: a mathematical modeling approach
- Author
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Romulus Breban
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Mathematical optimization ,Biology ,Models, Biological ,Article ,law.invention ,03 medical and health sciences ,0302 clinical medicine ,Cholera ,law ,Influenza, Human ,92D30 ,Humans ,Computer Simulation ,Vibrio cholerae ,Pathogen ,030304 developmental biology ,0303 health sciences ,Environmental transmission ,Applied Mathematics ,Direct transmission ,Environmental Exposure ,Orthomyxoviridae ,Agricultural and Biological Sciences (miscellaneous) ,Virology ,3. Good health ,93A30 ,Transmission (mechanics) ,Modeling and Simulation ,92D40 ,Environmental persistence ,Slow–fast dynamics ,030217 neurology & neurosurgery - Abstract
Although diseases such as influenza, tuberculosis and SARS are transmitted through an environmentally mediated mechanism, most modeling work on these topics is based on the concepts of infectious contact and direct transmission. In this paper we use a paradigm model to show that environmental transmission appears like direct transmission in the case where the pathogen persists little time in the environment. Furthermore, we formulate conditions for the validity of this modeling approximation and we illustrate them numerically for the cases of cholera and influenza. According to our results based on recently published parameter estimates, the direct transmission approximation fails for both cholera and influenza. While environmental transmission is typically chosen over direct transmission in modeling cholera, this is not the case for influenza.
- Published
- 2012
162. Using the building energy rating software for mathematically modelling operation costs in a simulated home
- Author
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Natividad Guadalajara and María José Ruá
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Operations research ,Total cost ,CONSTRUCCIONES ARQUITECTONICAS ,020209 energy ,cost model ,91B32 ,91B76 ,02 engineering and technology ,Software ,62J05 ,Cost model ,62P20 ,0202 electrical engineering, electronic engineering, information engineering ,Construction law ,Social cost ,energy performance in buildings ,Mathematics ,social cost ,Actuarial science ,Mathematical model ,Energy performance in buildings ,business.industry ,Applied Mathematics ,Depreciation ,Energy consumption ,ECONOMIA, SOCIOLOGIA Y POLITICA AGRARIA ,Regression ,Computer Science Applications ,private cost ,93A30 ,Computational Theory and Mathematics ,Service life ,ECONOMIA FINANCIERA Y CONTABILIDAD ,regression ,Private cost ,construction law ,business ,Energy (signal processing) - Abstract
The building industry is becoming very important in sustainable development. The recently developed policies in European Union directives on energy and their transposition to Spanish regulations make the Energy Performance Certification process for buildings mandatory. Two software tools have been developed in Spain to carry out this process: Lider and Calener. These software tools have been used in this paper to simulate energy performance in new semidetached houses after taking into account the thermal envelope of the building and facilities. This has been done in different climatic zones in Spain and for all the possible energy ratings. Based on the energy rating and construction cost variables, it has been possible to obtain mathematical models that explain the behaviour of global costs of buildings based on energy ratings and climatic zones. Depreciation costs, maintenance costs, energy consumption and CO2 emissions during the service life of a house have also been modelled.
- Published
- 2014
163. Approximately bisimilar symbolic models for nonlinear control systems
- Author
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Antoine Girard, Giordano Pola, Paulo Tabuada, Electrical Engineering Department [Los Angeles], University of California [Los Angeles] (UCLA), University of California-University of California, Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)
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0209 industrial biotechnology ,02 engineering and technology ,Nonlinear control ,Symbolic data analysis ,020901 industrial engineering & automation ,Supervisory control ,Approximate bisimulation ,Symbolic trajectory evaluation ,0202 electrical engineering, electronic engineering, information engineering ,FOS: Mathematics ,Nonlinear systems ,Electrical and Electronic Engineering ,Mathematics - Optimization and Control ,Mathematics ,Symbolic models ,Bisimulation ,Finite-state machine ,Continuous modelling ,Incremental stability ,93A30 ,Control and Systems Engineering ,Optimization and Control (math.OC) ,Control system ,020201 artificial intelligence & image processing ,Digital control systems ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Algorithm - Abstract
Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they are less suitable to describe software and hardware interfacing the physical world. For this reason there is a growing interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics, where each "symbol" corresponds to an "aggregate" of states in the continuous model. Since these symbolic models are of the same nature of the models used in computer science to describe software and hardware, they provide a unified language to study problems of control in which software and hardware interact with the physical world. Furthermore the use of symbolic models enables one to leverage techniques from supervisory control and algorithms from game theory for controller synthesis purposes. In this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent (bisimilar) to a symbolic model. The approximation error is a design parameter in the construction of the symbolic model and can be rendered as small as desired. Furthermore if the state space of the control system is bounded the obtained symbolic model is finite. For digital control systems, and under the stronger assumption of incremental input-to-state stability, symbolic models can be constructed through a suitable quantization of the inputs., Comment: Corrected typos
- Published
- 2008
164. A milling model with thermal effects including the dynamics of machine and work piece
- Author
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Rott, Oliver, Rasper, Patrick, Hömberg, Dietmar, and Uhlmann, Eckart
- Subjects
93A30 ,time domain simulation ,stability ,process machine interaction ,74H99 - Abstract
This paper deals with the development of a new mathematical model that characterizes the structure-process interaction for a complex milling system. The structure is divided into a work piece and a machine part, which are represented by different models. While the machine dynamics is characterized by a standard multi-body system, the work piece is described as a linear thermo-elastic continuum. The coupling of both parts is carried out by an empirical process model permitting an estimate of heat and coupling forces occurring during milling. This work reports the derivation of the governing equations emphasizing the coupling and summarizes the numerical algorithms being applied to solve the coupled equation system. The results of numerical simulations that show the dynamics of the complex thermo-mechanical system are presented at the end.
- Published
- 2008
- Full Text
- View/download PDF
165. Controller synthesis for bisimulation equivalence
- Author
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Paulo Tabuada
- Subjects
0209 industrial biotechnology ,Class (set theory) ,Theoretical computer science ,General Computer Science ,Computer science ,0102 computer and information sciences ,02 engineering and technology ,Nonlinear control ,Mathematical proof ,01 natural sciences ,020901 industrial engineering & automation ,Control theory ,FOS: Mathematics ,Electrical and Electronic Engineering ,Mathematics - Optimization and Control ,Bisimulation ,93A05 ,93A10 ,93A30 ,Generality ,Mechanical Engineering ,Optimization and Control (math.OC) ,010201 computation theory & mathematics ,Control and Systems Engineering ,Hybrid system ,Variety (universal algebra) - Abstract
The objective of this paper is to solve the controller synthesis problem for bisimulation equivalence in a wide variety of scenarios including discrete-event systems, nonlinear control systems, behavioral systems, hybrid systems and many others. This will be accomplished by showing that the arguments underlying proofs of existence and methods for the construction of controllers are extraneous to the particular class of systems being considered and thus can be presented in greater generality., Added references, comments and examples
- Published
- 2007
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