Pub Date : 1900-01-01DOI: 10.1137/1.9781611973273.22
I. Rosen, S. Luczak, Weiwei Hu, Michael Hankin
A scheme for the blind deconvolution of blood or breath alcohol concentration from biosensor measured transdermal alcohol concentration based on a parabolic PDE with Dirichlet boundary input and point-wise boundary output is developed. The estimation of the convolution filter corresponding to a particular patient and device is formulated as a nonlinear least squares fit to data. The deconvolution is then formulated as a regularized linear-quadratic programming problem. Numerical results involving patient data are pre-
{"title":"Discrete-Time Blind Deconvolution for Distributed Parameter Systems with Dirichlet Boundary Input and Unbounded Output with Application to a Transdermal Alcohol Biosensor","authors":"I. Rosen, S. Luczak, Weiwei Hu, Michael Hankin","doi":"10.1137/1.9781611973273.22","DOIUrl":"https://doi.org/10.1137/1.9781611973273.22","url":null,"abstract":"A scheme for the blind deconvolution of blood or breath alcohol concentration from biosensor measured transdermal alcohol concentration based on a parabolic PDE with Dirichlet boundary input and point-wise boundary output is developed. The estimation of the convolution filter corresponding to a particular patient and device is formulated as a nonlinear least squares fit to data. The deconvolution is then formulated as a regularized linear-quadratic programming problem. Numerical results involving patient data are pre-","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"110 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":"131178700","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: 10.1137/1.9781611974072.12
J. Wozniak, M. Firkowski
This paper continues the authors previous investigations of stability of the slowly rotating Timoshenko beam whose movement is controlled by the angular acceleration of the disk of the driving motor into which the beam is rigidly clamped. We consider the problem of optimal value of damping coefficient of a particular type of viscoelastic damping operator. To determine location of spectrum of an appropriate operator we use a transfer function method.
{"title":"Optimal damping coefficient of a slowly rotating Timoshenko beam","authors":"J. Wozniak, M. Firkowski","doi":"10.1137/1.9781611974072.12","DOIUrl":"https://doi.org/10.1137/1.9781611974072.12","url":null,"abstract":"This paper continues the authors previous investigations of stability of the slowly rotating Timoshenko beam whose movement is controlled by the angular acceleration of the disk of the driving motor into which the beam is rigidly clamped. We consider the problem of optimal value of damping coefficient of a particular type of viscoelastic damping operator. To determine location of spectrum of an appropriate operator we use a transfer function method.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"65 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":"131097856","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: 10.1137/1.9781611974072.44
M. Benosman, M. Xia
We present in this paper a preliminary result on extremum seeking (ES)-based adaptive trajectory tracking control for nonlinear systems. We propose, for the class of nonlinear systems with parametric uncertainties which can be rendered integral Input-to-State stable (iISS) w.r.t. the parameter estimation errors input, that it is possible to merge together the integral Input-to-State stabilizing feedback controller and a model-free extremum seeking algorithm to realize a learning-based indirect adaptive controller. We show the efficiency of this approach on a mechatronic example.
{"title":"Extremum Seeking-Based Indirect Adaptive Control for Nonlinear Systems with State-Dependent Uncertainties","authors":"M. Benosman, M. Xia","doi":"10.1137/1.9781611974072.44","DOIUrl":"https://doi.org/10.1137/1.9781611974072.44","url":null,"abstract":"We present in this paper a preliminary result on extremum seeking (ES)-based adaptive trajectory tracking control for nonlinear systems. We propose, for the class of nonlinear systems with parametric uncertainties which can be rendered integral Input-to-State stable (iISS) w.r.t. the parameter estimation errors input, that it is possible to merge together the integral Input-to-State stabilizing feedback controller and a model-free extremum seeking algorithm to realize a learning-based indirect adaptive controller. We show the efficiency of this approach on a mechatronic example.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"30 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":"123827959","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: 10.1137/1.9781611974072.33
A. Khurshudyan
We describe an approximate technique for solving the so– called mobile (scanning) control problems. The method is based on the Bubnov–Galerkin procedure and allows us to reduce the control problem, in which the unknown function is included in nonlinear manner, to a finite–dimensional system of integral constraints of equality type. An efficient numerical scheme is described reducing the solution of the nonlinear system to a problem of nonlinear programming. The proposed method is described thoroughly for nonlinear equations with linear boundary conditions. Two particular problems of heating by a moving source and vibration damping by a moving absorber are considered. The system of necessary and sufficient conditions for controllability are obtained in both cases. Main points of numerical implementations are discussed.
{"title":"On approximate solution of mobile (scanning) control problems","authors":"A. Khurshudyan","doi":"10.1137/1.9781611974072.33","DOIUrl":"https://doi.org/10.1137/1.9781611974072.33","url":null,"abstract":"We describe an approximate technique for solving the so– called mobile (scanning) control problems. The method is based on the Bubnov–Galerkin procedure and allows us to reduce the control problem, in which the unknown function is included in nonlinear manner, to a finite–dimensional system of integral constraints of equality type. An efficient numerical scheme is described reducing the solution of the nonlinear system to a problem of nonlinear programming. The proposed method is described thoroughly for nonlinear equations with linear boundary conditions. Two particular problems of heating by a moving source and vibration damping by a moving absorber are considered. The system of necessary and sufficient conditions for controllability are obtained in both cases. Main points of numerical implementations are discussed.","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":"114264020","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: 10.1137/1.9781611974072.30
Ghada Ben Belgacem, Chaker Jammazi
In this paper, the problem of finite-time boundary stabilization of two strings connected by point mass is investigated. Based on the so-called Riemann invariant transformation, the vibrating strings are transformed in two hybridhyperbolic systems, and leads to the posedness of our system. In order to act in the system, it is desirable to choose boundary feedbacks, in this case, Holderien stabilizing feedback laws to vanish in finite-time the right and the left of the solutions are considered.
{"title":"On the finite-time stabilization of strings connected by point mass","authors":"Ghada Ben Belgacem, Chaker Jammazi","doi":"10.1137/1.9781611974072.30","DOIUrl":"https://doi.org/10.1137/1.9781611974072.30","url":null,"abstract":"In this paper, the problem of finite-time boundary stabilization of two strings connected by point mass is investigated. Based on the so-called Riemann invariant transformation, the vibrating strings are transformed in two hybridhyperbolic systems, and leads to the posedness of our system. In order to act in the system, it is desirable to choose boundary feedbacks, in this case, Holderien stabilizing feedback laws to vanish in finite-time the right and the left of the solutions are considered.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"139 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":"121312220","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: 10.1137/1.9781611973273.20
Jun Liu, Yu Huang, Hai-wei Sun, M. Xiao
We develop high-order numerical methods for solving wave equations with van der Pol type nonlinear boundary conditions. Based on the wave reflection on the boundaries, we first solve the corresponding Riemann invariants by constructing two iterative mappings, and then, regarding the regularity of boundary conditions, propose two different high-order numerical approaches to the system. When the degree of regularity is high, we establish a sixth-order finite difference scheme. While for a low degree of regularity, we provide another method by utilizing the high-order GaussKronrod quadrature rule. Numerical experiments are performed to illustrate the proposed approaches.
提出了求解具有van der Pol型非线性边界条件的波动方程的高阶数值方法。基于波在边界上的反射，我们首先通过构造两个迭代映射来求解相应的Riemann不变量，然后针对边界条件的规律性，提出了两种不同的高阶数值方法。当正则度较高时，我们建立了六阶有限差分格式。而对于低正则度，我们提供了另一种方法，即利用高阶高斯ronrod正交规则。数值实验说明了所提出的方法。
{"title":"High-Order Numerical Methods for Wave Equations with van der Pol Type Boundary Conditions","authors":"Jun Liu, Yu Huang, Hai-wei Sun, M. Xiao","doi":"10.1137/1.9781611973273.20","DOIUrl":"https://doi.org/10.1137/1.9781611973273.20","url":null,"abstract":"We develop high-order numerical methods for solving wave equations with van der Pol type nonlinear boundary conditions. Based on the wave reflection on the boundaries, we first solve the corresponding Riemann invariants by constructing two iterative mappings, and then, regarding the regularity of boundary conditions, propose two different high-order numerical approaches to the system. When the degree of regularity is high, we establish a sixth-order finite difference scheme. While for a low degree of regularity, we provide another method by utilizing the high-order GaussKronrod quadrature rule. Numerical experiments are performed to illustrate the proposed approaches.","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":"129097004","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: 10.1137/1.9781611974072.57
Samir Sahyoun, S. Djouadi, K. Tomsovic, S. Lenhart
Large electrical power networks viewed as continuum systems have been studied under constant voltage magnitude assumptions. The continuum system phase behavior was proved to follow the dynamics of a second order nonlinear wave equation. The latter represents electromechanical wave propagation in large electric power networks. In this paper, we generalize this work to time and space variant voltage magnitudes which is the case in real world applications. The resulting partial differential equations (PDEs) are also wave equations but include more nonlinearity terms. Optimal control theory is used to derive optimality conditions for two optimal control problems. The first problem is when the mechanical power is the control input where the constraint is a constant voltage PDE, while the second problem is when the variant voltage magnitude is the control input under a generalized variant voltage PDE as the optimization constraint. Numerical results are presented to illustrate the performance of the resulting closed loop control systems for large power networks. Due to page size limits we present the optimal control results for the variant voltage swing PDE in a different paper.
{"title":"Optimal Distributed Control for Continuum Power Systems","authors":"Samir Sahyoun, S. Djouadi, K. Tomsovic, S. Lenhart","doi":"10.1137/1.9781611974072.57","DOIUrl":"https://doi.org/10.1137/1.9781611974072.57","url":null,"abstract":"Large electrical power networks viewed as continuum systems have been studied under constant voltage magnitude assumptions. The continuum system phase behavior was proved to follow the dynamics of a second order nonlinear wave equation. The latter represents electromechanical wave propagation in large electric power networks. In this paper, we generalize this work to time and space variant voltage magnitudes which is the case in real world applications. The resulting partial differential equations (PDEs) are also wave equations but include more nonlinearity terms. Optimal control theory is used to derive optimality conditions for two optimal control problems. The first problem is when the mechanical power is the control input where the constraint is a constant voltage PDE, while the second problem is when the variant voltage magnitude is the control input under a generalized variant voltage PDE as the optimization constraint. Numerical results are presented to illustrate the performance of the resulting closed loop control systems for large power networks. Due to page size limits we present the optimal control results for the variant voltage swing PDE in a different paper.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"37 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":"121366717","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: 10.1137/1.9781611974072.20
Shyh-Feng Chen
This paper deals with the problem of the output feedback H∞ control for discrete-time singular systems. Our goal is to develop a numerically tractable controller design method for output feedbackH∞ control of discrete-time singular systems. First, a new sufficient condition for H∞ performance is derived. Then, a sufficient condition for the existence of the desired output feedback H∞ controller is established. The proposed controller design method is formulated under the strict LMI framework. Finally, a numerical example is used to demonstrate the effectiveness of presented method.
{"title":"Output Feedback H∞ Control for Discrete-Time Singular Systems: A Strict LMI Approach","authors":"Shyh-Feng Chen","doi":"10.1137/1.9781611974072.20","DOIUrl":"https://doi.org/10.1137/1.9781611974072.20","url":null,"abstract":"This paper deals with the problem of the output feedback H∞ control for discrete-time singular systems. Our goal is to develop a numerically tractable controller design method for output feedbackH∞ control of discrete-time singular systems. First, a new sufficient condition for H∞ performance is derived. Then, a sufficient condition for the existence of the desired output feedback H∞ controller is established. The proposed controller design method is formulated under the strict LMI framework. Finally, a numerical example is used to demonstrate the effectiveness of presented method.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"23 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":"125480180","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: 10.1137/1.9781611974072.49
J. Almeida, L. T. Paiva, T. Mendonça, P. Rocha
Optimal control theory has gained increasing importance in biomedical applications, e.g., in the automatic administration of anesthetics during general anesthesia. In this context, one of the features that needs to be monitored is the depth of anesthesia. This is usually achieved by the joint administration of hypnotics and analgesics. The depth of anesthesia is quantified by the bispectral index that varies between 97.7% and 0%. This index should usually be kept at a reference level between 40% and 60% during surgeries with general anesthesia. In this contribution, we consider an open-loop control strategy to achieve this goal. In order to determine a suitable controller, we formulate a nonlinear optimal control problem and we solve it using direct methods. These methods have become increasingly useful when computing the numerical solution of an optimal control problem. Moreover, they are known to provide a very robust and general approach.
{"title":"Reference Tracking of Depth of Anesthesia Using Optimal Control","authors":"J. Almeida, L. T. Paiva, T. Mendonça, P. Rocha","doi":"10.1137/1.9781611974072.49","DOIUrl":"https://doi.org/10.1137/1.9781611974072.49","url":null,"abstract":"Optimal control theory has gained increasing importance in biomedical applications, e.g., in the automatic administration of anesthetics during general anesthesia. In this context, one of the features that needs to be monitored is the depth of anesthesia. This is usually achieved by the joint administration of hypnotics and analgesics. The depth of anesthesia is quantified by the bispectral index that varies between 97.7% and 0%. This index should usually be kept at a reference level between 40% and 60% during surgeries with general anesthesia. In this contribution, we consider an open-loop control strategy to achieve this goal. In order to determine a suitable controller, we formulate a nonlinear optimal control problem and we solve it using direct methods. These methods have become increasingly useful when computing the numerical solution of an optimal control problem. Moreover, they are known to provide a very robust and general approach.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"80 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":"124120764","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: 10.1137/1.9781611974072.3
M. Ishitobi, S. Kunimatsu
Normal forms called by Byrnes-Isidori are useful to study properties of zeros of systems in continuous-time and sampled-data domain for the design of feedback controllers. This paper investigates how transfer function matrices and state-space equations of linear square systems with controllability, observability and invertibility are transformed to normal forms. In addition, as an application of a normal form, an approximate expression of zeros of a sampled-data model corresponding to a continuous-time square system nondecouplable by static state feedback is derived for a small sampling period.
{"title":"Normal forms of linear multivariable square systems and their application","authors":"M. Ishitobi, S. Kunimatsu","doi":"10.1137/1.9781611974072.3","DOIUrl":"https://doi.org/10.1137/1.9781611974072.3","url":null,"abstract":"Normal forms called by Byrnes-Isidori are useful to study properties of zeros of systems in continuous-time and sampled-data domain for the design of feedback controllers. This paper investigates how transfer function matrices and state-space equations of linear square systems with controllability, observability and invertibility are transformed to normal forms. In addition, as an application of a normal form, an approximate expression of zeros of a sampled-data model corresponding to a continuous-time square system nondecouplable by static state feedback is derived for a small sampling period.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"50 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":"114974554","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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