Pub Date : 2015-07-08DOI: 10.1137/1.9781611974072.9
Taghreed MohammadRidha, C. Moog, E. Delaleau, M. Fliess, C. Join
The control design of an artificial pancreas, a hot research topic in diabetology, is tackled via the newly introduced model-free control and its corresponding "intelligent" proportional controller, which were already quite successful in many concrete and diverse situations. It results in an insulin injection for type 1 diabetes which displays via constant references a good nocturnal/fasting response, but unfortunately a poor postprandial behavior due to long hyperglycemia. When a variable reference is introduced, that switches between a constant one, when glycemia is more or less normal or moderate, and an exponential decay reference path, when a high glycemia rate indicates a meal intake, the results in silico, which employ real clinical data, become excellent. We obtain a bolus-shaped insulin injection rate during postprandial phases. The hyperglycemic peaks are therefore lowered a lot.
{"title":"A Variable Reference Trajectory for Model-Free Glycemia Regulation","authors":"Taghreed MohammadRidha, C. Moog, E. Delaleau, M. Fliess, C. Join","doi":"10.1137/1.9781611974072.9","DOIUrl":"https://doi.org/10.1137/1.9781611974072.9","url":null,"abstract":"The control design of an artificial pancreas, a hot research topic in diabetology, is tackled via the newly introduced model-free control and its corresponding \"intelligent\" proportional controller, which were already quite successful in many concrete and diverse situations. It results in an insulin injection for type 1 diabetes which displays via constant references a good nocturnal/fasting response, but unfortunately a poor postprandial behavior due to long hyperglycemia. When a variable reference is introduced, that switches between a constant one, when glycemia is more or less normal or moderate, and an exponential decay reference path, when a high glycemia rate indicates a meal intake, the results in silico, which employ real clinical data, become excellent. We obtain a bolus-shaped insulin injection rate during postprandial phases. The hyperglycemic peaks are therefore lowered a lot.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121241001","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 : 2015-07-08DOI: 10.1137/1.9781611974072.62
N. Boussaid, M. Caponigro, T. Chambrion
This note presents a positive approximate controllability result for a bilinear quantum system modeling a chemical bond. The main difficulties are due to the presence of a continuous spectrum part for the uncontrolled Hamiltonian (modeled by a Morse potential) and the unboundedness of the interaction potential (dipolar interaction). The proof is based on averaging technique and spectral analysis.
{"title":"An approximate controllability result with continuous spectrum: the Morse potential with dipolar interaction","authors":"N. Boussaid, M. Caponigro, T. Chambrion","doi":"10.1137/1.9781611974072.62","DOIUrl":"https://doi.org/10.1137/1.9781611974072.62","url":null,"abstract":"This note presents a positive approximate controllability result for a bilinear quantum system modeling a chemical bond. The main difficulties are due to the presence of a continuous spectrum part for the uncontrolled Hamiltonian (modeled by a Morse potential) and the unboundedness of the interaction potential (dipolar interaction). The proof is based on averaging technique and spectral analysis.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132529717","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 : 2015-07-01DOI: 10.1137/1.9781611974072.14
J. M. Igreja
Water canals for water delivery or irrigation provide a challenging system dynamics and control problem for distributed parameter plants. Canals are formed by a sequence of pools separated by gates. Output variables are the pool level at certain points, manipulated variables are the position of the gates and disturbances are the outlet water flows for agricultural use. Water pool dynamics are derived from the shallow water equations (also called Saint-Venant equations in its one-dimensional form) that are a set of hyperbolic partial differential nonlinear equations. Gate opening produces a water wave that travels through the pool which is partially reflected back in the next gate, the remainder crosses the gate and propagates to the next pool. Rigorous numerical methods that are able to capture water wave dynamics in canals are difficult to achieve. In this case a numerical routine was designed from a finite volume method for hyperbolic systems of conservation laws with source terms using a semi-discrete MUSCL flux reconstruction linear wellbalanced scheme (Kurganov and Tadmor central scheme with superbee limiter). Time integration was done with a Runge-Kutta method. The numerical method was used to simulate water dynamics in the first two pools with withdraws of an existing irrigation canal in Vila Nova de MilFontes, Portugal, including PI controlled gates movement to compensate for wave disturbances.
输水或灌溉的水渠为分布参数植物提供了一个具有挑战性的系统动力学和控制问题。运河是由一系列由门隔开的水池形成的。输出变量是某一点的水池水位，操纵变量是闸门的位置，干扰是农业用水的出口水流。浅水方程(也称为一维Saint-Venant方程)是一组双曲型偏微分非线性方程。闸门打开产生的水波穿过水池，部分反射回下一个闸门，其余部分穿过闸门，传播到下一个水池。能够捕捉运河中水波动力学的严格数值方法很难实现。在这种情况下，采用半离散MUSCL通量重建线性良好平衡格式(具有超级蜜蜂限位器的Kurganov和Tadmor中心格式)，从有限体积法设计了具有源项的双曲守恒律系统的数值程序。时间积分用龙格-库塔法完成。数值方法用于模拟葡萄牙Vila Nova de MilFontes现有灌溉渠的前两个水池的水动力学，包括PI控制闸门运动以补偿波浪扰动。
{"title":"Rigorous numerical method for irrigation canal system dynamics and control","authors":"J. M. Igreja","doi":"10.1137/1.9781611974072.14","DOIUrl":"https://doi.org/10.1137/1.9781611974072.14","url":null,"abstract":"Water canals for water delivery or irrigation provide a challenging system dynamics and control problem for distributed parameter plants. Canals are formed by a sequence of pools separated by gates. Output variables are the pool level at certain points, manipulated variables are the position of the gates and disturbances are the outlet water flows for agricultural use. Water pool dynamics are derived from the shallow water equations (also called Saint-Venant equations in its one-dimensional form) that are a set of hyperbolic partial differential nonlinear equations. Gate opening produces a water wave that travels through the pool which is partially reflected back in the next gate, the remainder crosses the gate and propagates to the next pool. Rigorous numerical methods that are able to capture water wave dynamics in canals are difficult to achieve. In this case a numerical routine was designed from a finite volume method for hyperbolic systems of conservation laws with source terms using a semi-discrete MUSCL flux reconstruction linear wellbalanced scheme (Kurganov and Tadmor central scheme with superbee limiter). Time integration was done with a Runge-Kutta method. The numerical method was used to simulate water dynamics in the first two pools with withdraws of an existing irrigation canal in Vila Nova de MilFontes, Portugal, including PI controlled gates movement to compensate for wave disturbances.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127483702","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 : 2015-06-08DOI: 10.1137/1.9781611974072.15
A. Knyazev, Y. Fujii, A. Malyshev
Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models and/or constraints. A Continuation/GMRES Method for NMPC, suggested by T. Ohtsuka in 2004, uses the GMRES iterative algorithm to solve a forward difference approximation $Ax=b$ of the Continuation NMPC (CNMPC) equations on every time step. The coefficient matrix $A$ of the linear system is often ill-conditioned, resulting in poor GMRES convergence, slowing down the on-line computation of the control by CNMPC, and reducing control quality. We adopt CNMPC for challenging minimum-time problems, and improve performance by introducing efficient preconditioning, utilizing parallel computing, and substituting MINRES for GMRES.
{"title":"Preconditioned Continuation Model Predictive Control","authors":"A. Knyazev, Y. Fujii, A. Malyshev","doi":"10.1137/1.9781611974072.15","DOIUrl":"https://doi.org/10.1137/1.9781611974072.15","url":null,"abstract":"Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models and/or constraints. A Continuation/GMRES Method for NMPC, suggested by T. Ohtsuka in 2004, uses the GMRES iterative algorithm to solve a forward difference approximation $Ax=b$ of the Continuation NMPC (CNMPC) equations on every time step. The coefficient matrix $A$ of the linear system is often ill-conditioned, resulting in poor GMRES convergence, slowing down the on-line computation of the control by CNMPC, and reducing control quality. We adopt CNMPC for challenging minimum-time problems, and improve performance by introducing efficient preconditioning, utilizing parallel computing, and substituting MINRES for GMRES.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"41 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114035090","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 : 2015-01-27DOI: 10.1137/1.9781611974072.39
D. Khlopin
The paper is concerned with two-person games with saddle point. We investigate the limits of value functions for long-time-average payoff, discounted average payoff, and the payoff that follows a probability density. Most of our assumptions restrict the dynamics of games. In particular, we assume the closedness of strategies under concatenation. It is also necessary for the value function to satisfy Bellman's optimality principle, even if in a weakened, asymptotic sense. We provide two results. The first one is a uniform Tauber result for games: if the value functions for long-time-average payoff converge uniformly, then there exists the uniform limit for probability densities from a sufficiently broad set; moreover, these limits coincide. The second one is the uniform Abel result: if a uniform limit for self-similar densities exists, then the uniform limit for long-time average payoff also exists, and they coincide.
{"title":"On asymptotic value for dynamic games with saddle point","authors":"D. Khlopin","doi":"10.1137/1.9781611974072.39","DOIUrl":"https://doi.org/10.1137/1.9781611974072.39","url":null,"abstract":"The paper is concerned with two-person games with saddle point. We investigate the limits of value functions for long-time-average payoff, discounted average payoff, and the payoff that follows a probability density. \u0000Most of our assumptions restrict the dynamics of games. In particular, we assume the closedness of strategies under concatenation. It is also necessary for the value function to satisfy Bellman's optimality principle, even if in a weakened, asymptotic sense. \u0000We provide two results. The first one is a uniform Tauber result for games: if the value functions for long-time-average payoff converge uniformly, then there exists the uniform limit for probability densities from a sufficiently broad set; moreover, these limits coincide. The second one is the uniform Abel result: if a uniform limit for self-similar densities exists, then the uniform limit for long-time average payoff also exists, and they coincide.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"57 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133420256","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 : 2013-07-08DOI: 10.1137/1.9781611973273.10
Yuting Chen, S. Trevezas, P. Cournède
The complexity of plant growth models and the scarcity of experimental data make the application of conventional data assimilation techniques rather difficult. In this paper, we use the Convolution Particle Filter (CPF) and an iterative adaptation, the Iterative Convolution Particle Filter (ICPF) for nonlinear parameter estimation. Both methods provide prior distributions in the Bayesian framework for data assimilation. CPF is sequentially used to update state and parameter estimates in order to improve model prediction and to assess the predictive uncertainty. The predictive performances of the two methods are evaluated by an application to the LNAS sugar beet growth model with three sets of real measurements, one used for parameter estimation and the two others used to test the model predictive capacity, both with and without data assimilation. Despite the low accuracy and the scarcity of the early data used for assimilation, the CPF-based data assimilation approach with the prior distribution based on ICPF estimations showed promising predictive capacities and provided robust confidence intervals. The method can therefore be considered as a potential candidate for yield prediction applications in agriculture.
{"title":"Iterative convolution particle filtering for nonlinear parameter estimation and data assimilation with application to crop yield prediction","authors":"Yuting Chen, S. Trevezas, P. Cournède","doi":"10.1137/1.9781611973273.10","DOIUrl":"https://doi.org/10.1137/1.9781611973273.10","url":null,"abstract":"The complexity of plant growth models and the scarcity of experimental data make the application of conventional data assimilation techniques rather difficult. In this paper, we use the Convolution Particle Filter (CPF) and an iterative adaptation, the Iterative Convolution Particle Filter (ICPF) for nonlinear parameter estimation. Both methods provide prior distributions in the Bayesian framework for data assimilation. CPF is sequentially used to update state and parameter estimates in order to improve model prediction and to assess the predictive uncertainty. The predictive performances of the two methods are evaluated by an application to the LNAS sugar beet growth model with three sets of real measurements, one used for parameter estimation and the two others used to test the model predictive capacity, both with and without data assimilation. Despite the low accuracy and the scarcity of the early data used for assimilation, the CPF-based data assimilation approach with the prior distribution based on ICPF estimations showed promising predictive capacities and provided robust confidence intervals. The method can therefore be considered as a potential candidate for yield prediction applications in agriculture.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"912 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126990279","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 : 2012-07-01DOI: 10.1137/1.9781611973273.1
Thomas Hunt, A. Krener
We present simplicial principal component analysis (SNPCA), a new manifold reconstruction algorithm that takes a set of data points lying near a lower dimensional manifold as input, possibly with noise, and extracts a simplicial complex that fits the data and the manifold. We have implemented the algorithm in the case where the input point cloud can be triangulated by a complex of 2-simplices, but is embedded in a space of arbitrary dimension. The algorithm is easily parallelizable. We are working to extend the algorithm to data sets lying on higher dimensional manifolds and more complex shapes, possibly of varying dimension. We provide the output of our algorithm for data that fall on the surface of a torus with and without noise, a swiss roll, and creased sheet, all embedded in R. We chose these manifolds to demonstrate that the algorithm does not require a smooth underlying manifold, or a manifold without boundary. We also discuss the theoretical justification of our algorithm.
{"title":"Simplicial Nonlinear Principal Component Analysis","authors":"Thomas Hunt, A. Krener","doi":"10.1137/1.9781611973273.1","DOIUrl":"https://doi.org/10.1137/1.9781611973273.1","url":null,"abstract":"We present simplicial principal component analysis (SNPCA), a new manifold reconstruction algorithm that takes a set of data points lying near a lower dimensional manifold as input, possibly with noise, and extracts a simplicial complex that fits the data and the manifold. We have implemented the algorithm in the case where the input point cloud can be triangulated by a complex of 2-simplices, but is embedded in a space of arbitrary dimension. The algorithm is easily parallelizable. We are working to extend the algorithm to data sets lying on higher dimensional manifolds and more complex shapes, possibly of varying dimension. We provide the output of our algorithm for data that fall on the surface of a torus with and without noise, a swiss roll, and creased sheet, all embedded in R. We chose these manifolds to demonstrate that the algorithm does not require a smooth underlying manifold, or a manifold without boundary. We also discuss the theoretical justification of our algorithm.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"160 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127399051","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: 10.1137/1.9781611973273.23
Sarah King, W. Kang, Liang Xu
In this paper we discuss a quantitative measure of partial observability for the shallow water equations. The quantity is consistent if approximated using well posed approximation schemes. A first order approximation of an unobservability index using empirical gramian is discussed. For linear systems with full state observability, the empirical gramian is equivalent to the observability gramian in control theory. We present algorithms for the computation of partial observability for the shallow water equations. These algorithms approximate the unobservability index using the empirical gramian via the nonlinear system and the linearized system given by the tangent linear model. This work has applications to optimal sensor placement for numerical weather prediction.
{"title":"Partial Observability for the Shallow Water Equations","authors":"Sarah King, W. Kang, Liang Xu","doi":"10.1137/1.9781611973273.23","DOIUrl":"https://doi.org/10.1137/1.9781611973273.23","url":null,"abstract":"In this paper we discuss a quantitative measure of partial observability for the shallow water equations. The quantity is consistent if approximated using well posed approximation schemes. A first order approximation of an unobservability index using empirical gramian is discussed. For linear systems with full state observability, the empirical gramian is equivalent to the observability gramian in control theory. We present algorithms for the computation of partial observability for the shallow water equations. These algorithms approximate the unobservability index using the empirical gramian via the nonlinear system and the linearized system given by the tangent linear model. This work has applications to optimal sensor placement for numerical weather prediction.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"10 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":"122338129","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: 10.1137/1.9781611974072.38
Farhad Farokhi, K. Johansson
We consider repeated routing games with piecewise-constant congestion taxing in which a central planner sets and announces the congestion taxes for fixed windows of time in advance. Specifically, c ...
{"title":"Using Piecewise-Constant Congestion Taxing Policy in Repeated Routing Games","authors":"Farhad Farokhi, K. Johansson","doi":"10.1137/1.9781611974072.38","DOIUrl":"https://doi.org/10.1137/1.9781611974072.38","url":null,"abstract":"We consider repeated routing games with piecewise-constant congestion taxing in which a central planner sets and announces the congestion taxes for fixed windows of time in advance. Specifically, c ...","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","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":"122036644","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: 10.1137/1.9781611974072.60
W. McEneaney, Amit P. Pandey
A game is considered where the communication network of the first player is explicitly modeled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modeled through expectations over idempotent probability measures. Idempotent algebras are used to obtain an algorithm for solution of the game.
{"title":"Development of an Idempotent Algorithm for a Network-Delay Game","authors":"W. McEneaney, Amit P. Pandey","doi":"10.1137/1.9781611974072.60","DOIUrl":"https://doi.org/10.1137/1.9781611974072.60","url":null,"abstract":"A game is considered where the communication network of the first player is explicitly modeled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modeled through expectations over idempotent probability measures. Idempotent algebras are used to obtain an algorithm for solution of the game.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","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":"131152569","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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