Pub Date : 2015-08-07DOI: 10.1137/1.9781611974072.34
G. Ciaramella
{"title":"Towards a minimum L2-norm exact control of the Pauli equation","authors":"G. Ciaramella","doi":"10.1137/1.9781611974072.34","DOIUrl":"https://doi.org/10.1137/1.9781611974072.34","url":null,"abstract":"","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115468324","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: 10.1137/1.9781611974072.4
Ghattassi Mohamed, M. Boutayeb, J. Roche
This contribution deals with state observer design for a class of PDE non linear systems described by Radiative transfer equation (RTE) coupled with nonlinear heat equation (NHE) in two dimensional domain. Observations are made though sensors placed at the upper boundary of the two dimensional domain. We explored the Galerkin method for a semi-discretization to obtain a large scale in finite dimensional. Thanks to the special structure of the obtained state system, we show through the Differential Mean Value Theorem (DMVT) that there always exists an observer gain matrix that assures asymptotic convergence. Both full order and reduced order state estimators are provided.
{"title":"On reduced order observer for radiative conductive heat transfer systems","authors":"Ghattassi Mohamed, M. Boutayeb, J. Roche","doi":"10.1137/1.9781611974072.4","DOIUrl":"https://doi.org/10.1137/1.9781611974072.4","url":null,"abstract":"This contribution deals with state observer design for a class of PDE non linear systems described by Radiative transfer equation (RTE) coupled with nonlinear heat equation (NHE) in two dimensional domain. Observations are made though sensors placed at the upper boundary of the two dimensional domain. We explored the Galerkin method for a semi-discretization to obtain a large scale in finite dimensional. Thanks to the special structure of the obtained state system, we show through the Differential Mean Value Theorem (DMVT) that there always exists an observer gain matrix that assures asymptotic convergence. Both full order and reduced order state estimators are provided.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"65 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":"123956777","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: 10.1137/1.9781611974072.2
Agostino Martinelli
This paper investigates the unknown input observability problem in the nonlinear case. Specifically, the systems here analyzed are characterized by dynamics that are nonlinear in the state and linear in the inputs and characterized by a single unknown input and multiple known inputs. Additionally, it is assumed that the unknown input is a differentiable function of time (up to a given order). The goal of the paper is not to design new observers but to provide a simple analytic condition in order to check the weak local observability of the state. In other words, the goal is to extend the well known observability rank condition to these systems. Specifically, the paper provides a simple algorithm to directly obtain the entire observable codistribution. As in the standard case of only known inputs, the observable codistribution is obtained by recursively computing the Lie derivatives along the vector fields that characterize the dynamics. However, in correspondence of the unknown input, the corresponding vector field must be suitably rescaled. Additionally, the Lie derivatives must be computed also along a new set of vector fields that are obtained by recursively performing suitable Lie bracketing of the vector fields that define the dynamics. In practice, the entire observable codistribution is obtained by a very simple recursive algorithm. However, the analytic derivations required to prove that this codistribution fully characterizes the weak local observability of the state are complex and, for the sake of brevity, are provided in a separate technical report. The proposed analytic approach is illustrated by checking the weak local observability of several nonlinear systems driven by known and unknown inputs.
{"title":"Nonlinear Unknown Input Observability: Analytical expression of the observable codistribution in the case of a single unknown input","authors":"Agostino Martinelli","doi":"10.1137/1.9781611974072.2","DOIUrl":"https://doi.org/10.1137/1.9781611974072.2","url":null,"abstract":"This paper investigates the unknown input observability problem in the nonlinear case. Specifically, the systems here analyzed are characterized by dynamics that are nonlinear in the state and linear in the inputs and characterized by a single unknown input and multiple known inputs. Additionally, it is assumed that the unknown input is a differentiable function of time (up to a given order). The goal of the paper is not to design new observers but to provide a simple analytic condition in order to check the weak local observability of the state. In other words, the goal is to extend the well known observability rank condition to these systems. Specifically, the paper provides a simple algorithm to directly obtain the entire observable codistribution. As in the standard case of only known inputs, the observable codistribution is obtained by recursively computing the Lie derivatives along the vector fields that characterize the dynamics. However, in correspondence of the unknown input, the corresponding vector field must be suitably rescaled. Additionally, the Lie derivatives must be computed also along a new set of vector fields that are obtained by recursively performing suitable Lie bracketing of the vector fields that define the dynamics. In practice, the entire observable codistribution is obtained by a very simple recursive algorithm. However, the analytic derivations required to prove that this codistribution fully characterizes the weak local observability of the state are complex and, for the sake of brevity, are provided in a separate technical report. The proposed analytic approach is illustrated by checking the weak local observability of several nonlinear systems driven by known and unknown inputs.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"308 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":"131682671","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: 10.1137/1.9781611974072.43
Petteri Laakkonen, A. Quadrat
We solve the robust regulation problem for single-input single-output plants by using the fractional ideal approach and without assuming the existence of coprime factorizations. In particular, we are able to formulate the famous internal model principle for stabilizable plants which do not necessarily admit coprime factorizations. We are able to give a necessary and sufficient solvability condition for the robust regulation problem, which leads to a design method for a robustly regulating controller. The theory is illustrated by examples.
{"title":"Robust Regulation of SISO Systems: The Fractional Ideal Approach","authors":"Petteri Laakkonen, A. Quadrat","doi":"10.1137/1.9781611974072.43","DOIUrl":"https://doi.org/10.1137/1.9781611974072.43","url":null,"abstract":"We solve the robust regulation problem for single-input single-output plants by using the fractional ideal approach and without assuming the existence of coprime factorizations. In particular, we are able to formulate the famous internal model principle for stabilizable plants which do not necessarily admit coprime factorizations. We are able to give a necessary and sufficient solvability condition for the robust regulation problem, which leads to a design method for a robustly regulating controller. The theory is illustrated by examples.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"60 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":"124479032","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: 10.1137/1.9781611974072.27
Ghattassi Mohamed, M. Boutayeb
This paper investigates the control problem for a class of highly nonlinear-coupled partial differential equations that describe radiative-conductive heat transfer systems. Thanks to the special structure of the obtained state system, using the Galerkin method for the semi-discretization of PDE and to the differential mean value theorem (DMVT), a new LMI condition is provided for the observer-based controller design. The observer and controller gain are computed simultaneously by solving linear matrix inequality (LMI), i.e a convex problem. Also we provide a reduced order observer based controller that assures global asymptotic stability.
{"title":"Observer based control for a class of coupled parabolic hyperbolic systems","authors":"Ghattassi Mohamed, M. Boutayeb","doi":"10.1137/1.9781611974072.27","DOIUrl":"https://doi.org/10.1137/1.9781611974072.27","url":null,"abstract":"This paper investigates the control problem for a class of highly nonlinear-coupled partial differential equations that describe radiative-conductive heat transfer systems. Thanks to the special structure of the obtained state system, using the Galerkin method for the semi-discretization of PDE and to the differential mean value theorem (DMVT), a new LMI condition is provided for the observer-based controller design. The observer and controller gain are computed simultaneously by solving linear matrix inequality (LMI), i.e a convex problem. Also we provide a reduced order observer based controller that assures global asymptotic stability.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"9 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":"122535110","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: 10.1137/1.9781611974072.29
E. Chambon, P. Apkarian, L. Burlion
The paper deals with the design of cooperative systems which formulates as computing a state coordinate transform such that the resulting dynamics are both stable and cooperative. The design of cooperative systems is a key problem to determine interval observers. Solutions are provided in the literature to transform any system into a cooperative system. A novel approach is proposed which reformulates into a stabilization problem. A solution is found using non-smooth optimization techniques.
{"title":"Metzler Matrix Transform Determination using a Nonsmooth Optimization Technique with an Application to Interval Observers","authors":"E. Chambon, P. Apkarian, L. Burlion","doi":"10.1137/1.9781611974072.29","DOIUrl":"https://doi.org/10.1137/1.9781611974072.29","url":null,"abstract":"The paper deals with the design of cooperative systems which formulates as computing a state coordinate transform such that the resulting dynamics are both stable and cooperative. The design of cooperative systems is a key problem to determine interval observers. Solutions are provided in the literature to transform any system into a cooperative system. A novel approach is proposed which reformulates into a stabilization problem. A solution is found using non-smooth optimization techniques.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"36 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":"122070043","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: 10.1137/1.9781611974072.10
Huu-Quan Do, M. Lenczner, R. Couturier, Y. Yakoubi
In a previous work, a theoretical framework of diffusive realization for state-realizations of some linear operators have been developed. Those are solutions to certain linear operator differential equations posed in one-dimensional bounded domains. They illustrate the theory on a Lyapunov equation arising from optimal control theory of the heat equation. In principle their method might be very efficient for real-time computation, however it is suffering from strong limitations. Here, we present significant improvements and report numerical results. A method of contour optimization is provided. It is based on a theoretical error estimate of the solution. Finally, we discuss expected gains if the method is implemented on different parallel computer topologies. The envisioned applications are for real-time distributed control on distributed computing architectures.
{"title":"Diffusive Realization of a Lyapunov Equation Solution, and Parallel Algorithms Implementation","authors":"Huu-Quan Do, M. Lenczner, R. Couturier, Y. Yakoubi","doi":"10.1137/1.9781611974072.10","DOIUrl":"https://doi.org/10.1137/1.9781611974072.10","url":null,"abstract":"In a previous work, a theoretical framework of diffusive realization for state-realizations of some linear operators have been developed. Those are solutions to certain linear operator differential equations posed in one-dimensional bounded domains. They illustrate the theory on a Lyapunov equation arising from optimal control theory of the heat equation. In principle their method might be very efficient for real-time computation, however it is suffering from strong limitations. Here, we present significant improvements and report numerical results. A method of contour optimization is provided. It is based on a theoretical error estimate of the solution. Finally, we discuss expected gains if the method is implemented on different parallel computer topologies. The envisioned applications are for real-time distributed control on distributed computing architectures.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"122 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":"116713824","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: 10.1137/1.9781611974072.37
Carole Louis-Rose
∂y1 ∂t − ∆y1 + f1(y1, y2) = kχω in Q, ∂y2 ∂t − ∆y2 + f2(y1, y2) = kχω in Q, y1 = y2 = 0 on Σ, y1(0) = y 0 1 , y2(0) = y 0 2 in Ω, where fi i = 1, 2, are functions of class C 1 on R, y i ∈ L (Ω) i = 1, 2, k ∈ L(G) represents the control function and χω is the characteristic function of ω, the set where the control is supported. The functions fi i = 1, 2 are assumed to be globally Lipschitz all along the paper, i.e. there exist Ji > 0, i = 1, 2 such that (1.2) |fi(x, y) − fi(z, u)| 6 Ji(‖x− z‖L2(Ω) + ‖y − u‖L2(Ω)), ∀x, y, z, u ∈ L(Ω). Such a system can be met in the field of mathematical biology; we refer to [1]. In this paper, we focus on a simultaneous null controllability problem with constrained state. Let (ej)j=1,...,m be a family of vectors of L(Q). Suppose that: (1.3) the vectors (ejχω)j=1,...,m are linearly independent.
∂y1∂t−∆y1 + f1 (y1, y2) = kχω在问,∂y2∂t−∆y2 k + f2 (y1, y2) =χω在问,y1Σ= y2 = 0, y1 (0) = y 0 1, y2 (0) = y为0 2Ω,fi i = 1, 2,在R C类的函数1,y我∈L(Ω)= 1,2 k∈L (G)代表了控制功能和χω是ω的特征函数,设置控制的支持。假设函数fi = 1,2在整篇论文中都是全局Lipschitz，即存在Ji > 0, i = 1,2，使得(1.2)|fi(x, y)−fi(z, u)| 6 Ji(‖x−z‖L2(Ω) +‖y−u‖L2(Ω))，∀x, y, z, u∈L(Ω)。这样的系统可以在数学生物学领域得到满足;我们参考[1]。本文主要研究一类具有约束状态的同时零可控性问题。让(ej) j = 1,…，m是L(Q)的向量族。设(1.3)向量(ejχω)j=1，…，m是线性无关的。
{"title":"Simultaneous null controllability of a semilinear system of parabolic equations","authors":"Carole Louis-Rose","doi":"10.1137/1.9781611974072.37","DOIUrl":"https://doi.org/10.1137/1.9781611974072.37","url":null,"abstract":" ∂y1 ∂t − ∆y1 + f1(y1, y2) = kχω in Q, ∂y2 ∂t − ∆y2 + f2(y1, y2) = kχω in Q, y1 = y2 = 0 on Σ, y1(0) = y 0 1 , y2(0) = y 0 2 in Ω, where fi i = 1, 2, are functions of class C 1 on R, y i ∈ L (Ω) i = 1, 2, k ∈ L(G) represents the control function and χω is the characteristic function of ω, the set where the control is supported. The functions fi i = 1, 2 are assumed to be globally Lipschitz all along the paper, i.e. there exist Ji > 0, i = 1, 2 such that (1.2) |fi(x, y) − fi(z, u)| 6 Ji(‖x− z‖L2(Ω) + ‖y − u‖L2(Ω)), ∀x, y, z, u ∈ L(Ω). Such a system can be met in the field of mathematical biology; we refer to [1]. In this paper, we focus on a simultaneous null controllability problem with constrained state. Let (ej)j=1,...,m be a family of vectors of L(Q). Suppose that: (1.3) the vectors (ejχω)j=1,...,m are linearly independent.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"9 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":"132234946","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: 10.1137/1.9781611974072.1
C. Cárdenas, J. Loiseau, C. Martinez
The concept of (A, B)-invariant subspace is the fundamental concept of the geometric approach of control design. It has been extended by many authors to that of (A, B)-invariant module or semimodule, for the sake of extending the solution of various control problems to the case of systems over rings or semi rings. In this paper is discussed the use of dynamic feedback control laws for systems over semirings, and it is shown that an (A, B)-invariant semimodule over a commutative semiring can be made invariant for the closed-loop system by dynamic feedback.
{"title":"Controlled Invariance and Dynamic Feedback for Systems over Semirings","authors":"C. Cárdenas, J. Loiseau, C. Martinez","doi":"10.1137/1.9781611974072.1","DOIUrl":"https://doi.org/10.1137/1.9781611974072.1","url":null,"abstract":"The concept of (A, B)-invariant subspace is the fundamental concept of the geometric approach of control design. It has been extended by many authors to that of (A, B)-invariant module or semimodule, for the sake of extending the solution of various control problems to the case of systems over rings or semi rings. In this paper is discussed the use of dynamic feedback control laws for systems over semirings, and it is shown that an (A, B)-invariant semimodule over a commutative semiring can be made invariant for the closed-loop system by dynamic feedback.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"35 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":"126907654","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: 10.1137/1.9781611974072.48
M. Chyba, J. Coron, Pierre Gabriel, Yuriy Mileyko, H. Rezaei
The goal is to establish a kinetic model of amyloid formation which will take into account the contribution of fragmentation to the de novo creation of templating interfaces. We propose a new, more comprehensive mathematical model which takes into account previously neglected phenomena potentially occurring during the templating and fragmentation processes. In particular, we try to capture a potential effect of the topology and geometry of prion folding on the elongation and fragmentation properties of a polymer of a given length by separating polymers of the same length into several compartments. Additionally, we apply techniques from geometric control to the new model to design optimal strategies for accelerating the current amplification protocols, such as the Protein Misfolding Cyclic Amplification (PMCA). The objective is to reduce the time needed to diagnose many neurodegenerative diseases. Determining the optimal strategy for accelerated replication in the general problem of fragmentation optimization is still an open question.
{"title":"Identification of the Fragmentation Role in the Amyloid Assembling Processes and Application to their Optimization","authors":"M. Chyba, J. Coron, Pierre Gabriel, Yuriy Mileyko, H. Rezaei","doi":"10.1137/1.9781611974072.48","DOIUrl":"https://doi.org/10.1137/1.9781611974072.48","url":null,"abstract":"The goal is to establish a kinetic model of amyloid formation which will take into account the contribution of fragmentation to the de novo creation of templating interfaces. We propose a new, more comprehensive mathematical model which takes into account previously neglected phenomena potentially occurring during the templating and fragmentation processes. In particular, we try to capture a potential effect of the topology and geometry of prion folding on the elongation and fragmentation properties of a polymer of a given length by separating polymers of the same length into several compartments. Additionally, we apply techniques from geometric control to the new model to design optimal strategies for accelerating the current amplification protocols, such as the Protein Misfolding Cyclic Amplification (PMCA). The objective is to reduce the time needed to diagnose many neurodegenerative diseases. Determining the optimal strategy for accelerated replication in the general problem of fragmentation optimization is still an open question.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"32 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":"122173477","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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