Pub Date : 2013-09-04DOI: 10.3182/20130904-3-FR-2041.00123
Yingchong Ma, G. Zheng, W. Perruquetti
This paper presents the real-time identification of different types of non-holonomic mobile robot systems. Since the robot type is a priori unknown, the robot systems are formulated as a switched singular nonlinear system, and the problem becomes the real-time identification of the switching signal, and then the existence of the input-output functions and the distinguishability of the system are studied. We show in the simulations that the proposed technique is implemented easily and effectively, and it is robust to the noises as well.
{"title":"Identification of Different Types of Non-Holonomic Mobile Robots","authors":"Yingchong Ma, G. Zheng, W. Perruquetti","doi":"10.3182/20130904-3-FR-2041.00123","DOIUrl":"https://doi.org/10.3182/20130904-3-FR-2041.00123","url":null,"abstract":"This paper presents the real-time identification of different types of non-holonomic mobile robot systems. Since the robot type is a priori unknown, the robot systems are formulated as a switched singular nonlinear system, and the problem becomes the real-time identification of the switching signal, and then the existence of the input-output functions and the distinguishability of the system are studied. We show in the simulations that the proposed technique is implemented easily and effectively, and it is robust to the noises as well.","PeriodicalId":420241,"journal":{"name":"IFAC Symposium on Nonlinear Control Systems","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115732634","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 : 2013-09-04DOI: 10.3182/20130904-3-FR-2041.00045
C. Casenave, D. Dochain, G. Alvarez, M. Arellano, H. Benkhelifa, D. Leducq
In the ice cream industry, the type of final desired product (large cartons (sqrounds) or ice creams on a stick) determine the viscosity at which the ice cream has to be produced. One of the objectives of the ice cream crystallization processes is therefore to produce an ice cream of specified viscosity. In this paper, a nonlinear control strategy is proposed for the control of the viscosity of the ice cream in a continuous crystallizer. It has been designed on the basis of a reduced order model obtained by application of the method of moments, on a population balance equation describing the evolution of the crystal size distribution. The control strategy is based on a linearizing control law coupled with a Smith predictor to account for the measurement delay. It has been validated on a pilot plant located at IRSTEA (Antony, France).
{"title":"Control of a Nonlinear Ice Cream Crystallization Process","authors":"C. Casenave, D. Dochain, G. Alvarez, M. Arellano, H. Benkhelifa, D. Leducq","doi":"10.3182/20130904-3-FR-2041.00045","DOIUrl":"https://doi.org/10.3182/20130904-3-FR-2041.00045","url":null,"abstract":"In the ice cream industry, the type of final desired product (large cartons (sqrounds) or ice creams on a stick) determine the viscosity at which the ice cream has to be produced. One of the objectives of the ice cream crystallization processes is therefore to produce an ice cream of specified viscosity. In this paper, a nonlinear control strategy is proposed for the control of the viscosity of the ice cream in a continuous crystallizer. It has been designed on the basis of a reduced order model obtained by application of the method of moments, on a population balance equation describing the evolution of the crystal size distribution. The control strategy is based on a linearizing control law coupled with a Smith predictor to account for the measurement delay. It has been validated on a pilot plant located at IRSTEA (Antony, France).","PeriodicalId":420241,"journal":{"name":"IFAC Symposium on Nonlinear Control Systems","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115588230","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 : 2013-09-04DOI: 10.3182/20130904-3-FR-2041.00066
M. J. Lacerda, S. Tarbouriech, G. García, P. Peres
This paper is concerned with the problem of H∞ filtering for continuous-time nonlinear quadratic systems. The aim is to design a full order dynamic fi lter that can also contain quadratic terms. The strategy relies on the use of a quadratic Lyapunov function and an inequality condition that assures an H∞ performance bound for the augmented quadratic system, composed by the original system and the filter to be designed, in a regional (local) context. Then , by using the Finsler's lemma, an enlarged parameter space is created, where the Lyapunov matrix appears separated from the system matrices. Imposing structural constraints to the decision variables , theoretical conditions, which can be treated as linear matrix inequality conditions by fixing a grid on a sc alar parameter, can be derived for the filter design. As illustrated by numerical experiments, the proposed conditions can improve the H∞ performance provided by linear filters by including the quad ratic terms in the filter dynamics.
{"title":"H-Infinity Filter Design for Nonlinear Quadratic Systems","authors":"M. J. Lacerda, S. Tarbouriech, G. García, P. Peres","doi":"10.3182/20130904-3-FR-2041.00066","DOIUrl":"https://doi.org/10.3182/20130904-3-FR-2041.00066","url":null,"abstract":"This paper is concerned with the problem of H∞ filtering for continuous-time nonlinear quadratic systems. The aim is to design a full order dynamic fi lter that can also contain quadratic terms. The strategy relies on the use of a quadratic Lyapunov function and an inequality condition that assures an H∞ performance bound for the augmented quadratic system, composed by the original system and the filter to be designed, in a regional (local) context. Then , by using the Finsler's lemma, an enlarged parameter space is created, where the Lyapunov matrix appears separated from the system matrices. Imposing structural constraints to the decision variables , theoretical conditions, which can be treated as linear matrix inequality conditions by fixing a grid on a sc alar parameter, can be derived for the filter design. As illustrated by numerical experiments, the proposed conditions can improve the H∞ performance provided by linear filters by including the quad ratic terms in the filter dynamics.","PeriodicalId":420241,"journal":{"name":"IFAC Symposium on Nonlinear Control Systems","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122342996","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 : 1900-01-01DOI: 10.3182/20130904-3-FR-2041.00148
M. Halás, C. Moog
In this paper the concept of eigenvalues and eigenvectors of nonlinear systems, both continuous- and discrete-time, is suggested. It represents a generalization of the concept known from linear control theory. Some basic properties, like invariance of eigenvalues under a (nonlinear) change of coordinates, possibility to transform the system to the diagonal form and, respectively, to the feedforward form are then shown.
{"title":"Definition of Eigenvalues for a Nonlinear System","authors":"M. Halás, C. Moog","doi":"10.3182/20130904-3-FR-2041.00148","DOIUrl":"https://doi.org/10.3182/20130904-3-FR-2041.00148","url":null,"abstract":"In this paper the concept of eigenvalues and eigenvectors of nonlinear systems, both continuous- and discrete-time, is suggested. It represents a generalization of the concept known from linear control theory. Some basic properties, like invariance of eigenvalues under a (nonlinear) change of coordinates, possibility to transform the system to the diagonal form and, respectively, to the feedforward form are then shown.","PeriodicalId":420241,"journal":{"name":"IFAC Symposium on Nonlinear Control Systems","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122073839","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 : 1900-01-01DOI: 10.3182/20130904-3-FR-2041.00010
A. Bacciotti
Abstract In this note we prove that if a switched system F formed by a pair of linear vector fields of R 2 is asymptotically controllable, then the discrete time operator associated to F admits at least one real eigenvalue λ, with |λ|
{"title":"A Remark about Linear Switched Systems in the Plane","authors":"A. Bacciotti","doi":"10.3182/20130904-3-FR-2041.00010","DOIUrl":"https://doi.org/10.3182/20130904-3-FR-2041.00010","url":null,"abstract":"Abstract In this note we prove that if a switched system F formed by a pair of linear vector fields of R 2 is asymptotically controllable, then the discrete time operator associated to F admits at least one real eigenvalue λ, with |λ|","PeriodicalId":420241,"journal":{"name":"IFAC Symposium on Nonlinear Control Systems","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134207675","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 : 1900-01-01DOI: 10.3182/20130904-3-FR-2041.00014
Hakki Ulaş Ünal, W. Michiels
Abstract We present an approach which allows to accurately predict both the occurrence and type of partially synchronous regimes of delay-coupled non-linear oscillators. Unlike the conventional approach, we build on an analysis of the stability properties of the synchronized equilibrium in the (coupling gain, delay) parameter space. As partially synchronous regimes are closely related to the presence of invariant manifolds, we first present necessary and sufficient conditions for the existence of forward invariant sets. Next, from the existence of these invariant sets and from the characterization of solutions in the unstable manifold of the synchronized equilibrium, we predict which (gain, delay) parameters may result in fully/partially synchronous behavior. We illustrate the approach for a network of delay coupled Hindmarsh-Rose neurons.
{"title":"Prediction of Partially Synchronous Regimes of Delay-Coupled Nonlinear Oscillators","authors":"Hakki Ulaş Ünal, W. Michiels","doi":"10.3182/20130904-3-FR-2041.00014","DOIUrl":"https://doi.org/10.3182/20130904-3-FR-2041.00014","url":null,"abstract":"Abstract We present an approach which allows to accurately predict both the occurrence and type of partially synchronous regimes of delay-coupled non-linear oscillators. Unlike the conventional approach, we build on an analysis of the stability properties of the synchronized equilibrium in the (coupling gain, delay) parameter space. As partially synchronous regimes are closely related to the presence of invariant manifolds, we first present necessary and sufficient conditions for the existence of forward invariant sets. Next, from the existence of these invariant sets and from the characterization of solutions in the unstable manifold of the synchronized equilibrium, we predict which (gain, delay) parameters may result in fully/partially synchronous behavior. We illustrate the approach for a network of delay coupled Hindmarsh-Rose neurons.","PeriodicalId":420241,"journal":{"name":"IFAC Symposium on Nonlinear Control Systems","volume":"243 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124682678","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 : 1900-01-01DOI: 10.3182/20130904-3-FR-2041.00205
A. Proskurnikov
Abstract The problem of synchronization (consensus) in nonlinearly coupled network is addressed. The agents of the network are assumed to identical and linear, however, they may have arbitrary order and be unstable. The interaction topology may switch and the couplings are uncertain, assumed only to satisfy conventional quadratic constraints. We offer easily verifiable synchronization criteria, based on the Kalman-Yakubovich-Popov lemma and extending a number of known result for agents with special dynamics. Those criteria are close in spirit to the celebrated circle criterion for the stability of Lurie systems.
{"title":"The Circle Criterion for Synchronization in Nonlinearly Coupled Networks","authors":"A. Proskurnikov","doi":"10.3182/20130904-3-FR-2041.00205","DOIUrl":"https://doi.org/10.3182/20130904-3-FR-2041.00205","url":null,"abstract":"Abstract The problem of synchronization (consensus) in nonlinearly coupled network is addressed. The agents of the network are assumed to identical and linear, however, they may have arbitrary order and be unstable. The interaction topology may switch and the couplings are uncertain, assumed only to satisfy conventional quadratic constraints. We offer easily verifiable synchronization criteria, based on the Kalman-Yakubovich-Popov lemma and extending a number of known result for agents with special dynamics. Those criteria are close in spirit to the celebrated circle criterion for the stability of Lurie systems.","PeriodicalId":420241,"journal":{"name":"IFAC Symposium on Nonlinear Control Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130933213","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 : 1900-01-01DOI: 10.3182/20130904-3-FR-2041.00100
Y. Kawano, T. Ohtsuka
In the linear control theory, the observability Popov-Belevitch-Hautus (PBH) test plays an important role in studying observability along with the observability rank condition and observability Gramian. The observability rank condition and observability Gramian have been extended to nonlinear systems and have found applications in the analysis of nonlinear systems. On the other hand, there is no observability criterion for nonlinear systems corresponding to the PBH test. In this study, we generalize the observability PBH test for nonlinear systems using pseudo-linear transformation.
{"title":"Observability Analysis of Nonlinear Systems Using Pseudo-Linear Transformation","authors":"Y. Kawano, T. Ohtsuka","doi":"10.3182/20130904-3-FR-2041.00100","DOIUrl":"https://doi.org/10.3182/20130904-3-FR-2041.00100","url":null,"abstract":"In the linear control theory, the observability Popov-Belevitch-Hautus (PBH) test plays an important role in studying observability along with the observability rank condition and observability Gramian. The observability rank condition and observability Gramian have been extended to nonlinear systems and have found applications in the analysis of nonlinear systems. On the other hand, there is no observability criterion for nonlinear systems corresponding to the PBH test. In this study, we generalize the observability PBH test for nonlinear systems using pseudo-linear transformation.","PeriodicalId":420241,"journal":{"name":"IFAC Symposium on Nonlinear Control Systems","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126768008","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 : 1900-01-01DOI: 10.3182/20130904-3-FR-2041.00114
Valter J. S. Leite, S. Tarbouriech, G. García
Abstract The main objective in this paper is to investigate the robust performance degradation for a class of nonlinear systems due to some dynamics that are not taken into account during the controller design stage. This is usually the case in practical applications where a simplified (nonlinear) model is used to design the controller. Therefore, it is expected some performance degradation in the application of such a controller due to the presence of the neglected dynamics. With this purpose, some convex conditions for stability analysis and energy-peak evaluation of nonlinear control systems are given. It is supposed that the nonlinear functions present in the model are subject to bounded uncertainties and that both the simplified model and the neglected dynamics model are affected by polytopic uncertainties. The theoretical conditions providing stability and energy-peak bound on the regulated output of the system despite the presence of uncertainties associated with the nonlinear functions are obtained by means of a parameter dependent Lyapunov function. The proposal is illustrated by numerical examples.
{"title":"Energy-Peak Evaluation of Nonlinear Control Systems under Neglected Dynamics","authors":"Valter J. S. Leite, S. Tarbouriech, G. García","doi":"10.3182/20130904-3-FR-2041.00114","DOIUrl":"https://doi.org/10.3182/20130904-3-FR-2041.00114","url":null,"abstract":"Abstract The main objective in this paper is to investigate the robust performance degradation for a class of nonlinear systems due to some dynamics that are not taken into account during the controller design stage. This is usually the case in practical applications where a simplified (nonlinear) model is used to design the controller. Therefore, it is expected some performance degradation in the application of such a controller due to the presence of the neglected dynamics. With this purpose, some convex conditions for stability analysis and energy-peak evaluation of nonlinear control systems are given. It is supposed that the nonlinear functions present in the model are subject to bounded uncertainties and that both the simplified model and the neglected dynamics model are affected by polytopic uncertainties. The theoretical conditions providing stability and energy-peak bound on the regulated output of the system despite the presence of uncertainties associated with the nonlinear functions are obtained by means of a parameter dependent Lyapunov function. The proposal is illustrated by numerical examples.","PeriodicalId":420241,"journal":{"name":"IFAC Symposium on Nonlinear Control Systems","volume":"175 1-3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116637887","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 : 1900-01-01DOI: 10.3182/20130904-3-FR-2041.00200
Tetsuya Ishikawa, T. Hayakawa
Abstract In recent years, it becomes important to understand chaotic behaviors in order to analyze nonlinear dynamics because chaotic behavior can be observed in many models in the field of physics, biology, and so on. To understand chaotic behaviors, investigating mechanisms of chaos is necessary and it is meaningful to study simple models that shows chaotic behaviors. In this paper, we propose an extremely simple triangle folding map and show that the map has k -periodic points for any integer k , and show the map has sensitivity to initial conditions. Finally, we discuss the connection with the Sierpinski gasket and construct similar types of fractal geometry.
{"title":"Chaotic Behavior of the Folding Map on the Equilateral Triangle","authors":"Tetsuya Ishikawa, T. Hayakawa","doi":"10.3182/20130904-3-FR-2041.00200","DOIUrl":"https://doi.org/10.3182/20130904-3-FR-2041.00200","url":null,"abstract":"Abstract In recent years, it becomes important to understand chaotic behaviors in order to analyze nonlinear dynamics because chaotic behavior can be observed in many models in the field of physics, biology, and so on. To understand chaotic behaviors, investigating mechanisms of chaos is necessary and it is meaningful to study simple models that shows chaotic behaviors. In this paper, we propose an extremely simple triangle folding map and show that the map has k -periodic points for any integer k , and show the map has sensitivity to initial conditions. Finally, we discuss the connection with the Sierpinski gasket and construct similar types of fractal geometry.","PeriodicalId":420241,"journal":{"name":"IFAC Symposium on Nonlinear Control Systems","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121582186","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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