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Mathematics of Control Signals and Systems最新文献

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On the controllability of a system coupling Kuramoto–Sivashinsky–Korteweg–de Vries and transport equations 论库拉莫斯-西瓦辛斯基-科特韦格-德弗里斯与输运方程耦合系统的可控性
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-06-23 DOI: 10.1007/s00498-024-00390-9
Manish Kumar, Subrata Majumdar
{"title":"On the controllability of a system coupling Kuramoto–Sivashinsky–Korteweg–de Vries and transport equations","authors":"Manish Kumar, Subrata Majumdar","doi":"10.1007/s00498-024-00390-9","DOIUrl":"https://doi.org/10.1007/s00498-024-00390-9","url":null,"abstract":"<p>In this paper, we study the null controllability of a coupled parabolic–hyperbolic system in one dimension with a single control using the moment method. More precisely, we consider a system coupling Kuramoto–Sivashinsky–Korteweg–de Vries equation and transport equation through first-order derivatives. We explore the null controllability of four different control systems with the control acting either on the periodic boundary or in some open subset of the interior of the domain with periodic boundary conditions. Depending on the position of the control, we get some regular periodic Sobolev space as the space of initial data for which the null controllability holds, provided the time is sufficiently large.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"88 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain 基于数据驱动的时域端口-哈密尔顿系统的邻接校准
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-06-06 DOI: 10.1007/s00498-024-00389-2
Michael Günther, Birgit Jacob, Claudia Totzeck
{"title":"Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain","authors":"Michael Günther, Birgit Jacob, Claudia Totzeck","doi":"10.1007/s00498-024-00389-2","DOIUrl":"https://doi.org/10.1007/s00498-024-00389-2","url":null,"abstract":"<p>We present a gradient-based calibration algorithm to identify the system matrices of a linear port-Hamiltonian system from given input–output time data. Aiming for a direct structure-preserving approach, we employ techniques from optimal control with ordinary differential equations and define a constrained optimization problem. The input-to-state stability is discussed which is the key step towards the existence of optimal controls. Further, we derive the first-order optimality system taking into account the port-Hamiltonian structure. Indeed, the proposed method preserves the skew symmetry and positive (semi)-definiteness of the system matrices throughout the optimization iterations. Numerical results with perturbed and unperturbed synthetic data, as well as an example from the PHS benchmark collection [17] demonstrate the feasibility of the approach.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"41 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generic observability for port-Hamiltonian descriptor systems 端口-哈密尔顿描述子系统的通用可观测性
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-06-03 DOI: 10.1007/s00498-024-00388-3
Jonas Kirchhoff
{"title":"Generic observability for port-Hamiltonian descriptor systems","authors":"Jonas Kirchhoff","doi":"10.1007/s00498-024-00388-3","DOIUrl":"https://doi.org/10.1007/s00498-024-00388-3","url":null,"abstract":"<p>The present work is a successor of Ilchmann and Kirchhoff (Math Control Signals Syst 33:359–377, 2021. https://doi.org/10.1007/s00498-021-00287-x), Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2023. https://doi.org/10.1007/s00498-021-00287-x) on (relative) generic controllability of unstructured linear differential-algebraic systems and of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) on (relative) generic controllability of port-Hamiltonian descriptor systems. We extend their results to (relative) genericity of observability. For unstructured differential-algebraic systems, criteria for (relative) generic observability are derived from Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2023. https://doi.org/10.1007/s00498-021-00287-x) using duality. This is not possible for port-Hamiltonian systems. Hence, we tweak the results of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) and derive similar criteria as for the unstructured case. Additionally, we consider certain rank constraints on the system matrices.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"70 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Operator-valued multiplier theorems for causal translation-invariant operators with applications to control theoretic input-output stability 因果平移不变算子的算子值乘数定理及其在控制理论输入输出稳定性中的应用
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-05-30 DOI: 10.1007/s00498-024-00387-4
Chris Guiver, Hartmut Logemann, Mark R. Opmeer
{"title":"Operator-valued multiplier theorems for causal translation-invariant operators with applications to control theoretic input-output stability","authors":"Chris Guiver, Hartmut Logemann, Mark R. Opmeer","doi":"10.1007/s00498-024-00387-4","DOIUrl":"https://doi.org/10.1007/s00498-024-00387-4","url":null,"abstract":"<p>We prove an operator-valued Laplace multiplier theorem for causal translation-invariant linear operators which provides a characterization of continuity from <span>(H^alpha ({mathbb {R}},U))</span> to <span>(H^beta ({mathbb {R}},U))</span> (fractional <i>U</i>-valued Sobolev spaces, <i>U</i> a complex Hilbert space) in terms of a certain boundedness property of the transfer function (or symbol), an operator-valued holomorphic function on the right-half of the complex plane. We identify sufficient conditions under which this boundedness property is equivalent to a similar property of the boundary function of the transfer function. Under the assumption that <i>U</i> is separable, the Laplace multiplier theorem is used to derive a Fourier multiplier theorem. We provide an application to mathematical control theory, by developing a novel input-output stability framework for a large class of causal translation-invariant linear operators which refines existing input-output stability theories. Furthermore, we show how our work is linked to the theory of well-posed linear systems and to results on polynomial stability of operator semigroups. Several examples are discussed in some detail.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"35 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Necessary conditions for turnpike property for generalized linear–quadratic problems 广义线性二次型问题拐点性质的必要条件
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-04-17 DOI: 10.1007/s00498-024-00385-6
Roberto Guglielmi, Zhuqing Li
{"title":"Necessary conditions for turnpike property for generalized linear–quadratic problems","authors":"Roberto Guglielmi, Zhuqing Li","doi":"10.1007/s00498-024-00385-6","DOIUrl":"https://doi.org/10.1007/s00498-024-00385-6","url":null,"abstract":"<p>In this paper, we develop several necessary conditions of turnpike property for generalized linear–quadratic (LQ) optimal control problem in infinite-dimensional setting. The term ‘generalized’ here means that both quadratic and linear terms are considered in the running cost. The turnpike property reflects the fact that over a sufficiently large time horizon, the optimal trajectories and optimal controls stay for most of the time close to a steady state of the system. We show that the turnpike property is strongly connected to certain system theoretical properties of the control system. We provide suitable conditions to characterize the turnpike property in terms of the detectability and stabilizability of the system. Subsequently, we show the equivalence between the exponential turnpike property for generalized LQ and LQ optimal control problems.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"45 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140612253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Manifold turnpikes of nonlinear port-Hamiltonian descriptor systems under minimal energy supply 最小能量供给下非线性端口-哈密尔顿描述子系统的曼弗雷德转折点
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-04-09 DOI: 10.1007/s00498-024-00384-7
Attila Karsai
{"title":"Manifold turnpikes of nonlinear port-Hamiltonian descriptor systems under minimal energy supply","authors":"Attila Karsai","doi":"10.1007/s00498-024-00384-7","DOIUrl":"https://doi.org/10.1007/s00498-024-00384-7","url":null,"abstract":"<p>Turnpike phenomena of nonlinear port-Hamiltonian descriptor systems under minimal energy supply are studied. Under assumptions on the smoothness of the system nonlinearities, it is shown that the optimal control problem is dissipative with respect to a manifold. Then, under controllability assumptions, it is shown that the optimal control problem exhibits a manifold turnpike property.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"214 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140596261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Boundary controllability for a 1D degenerate parabolic equation with a Robin boundary condition 具有罗宾边界条件的一维退化抛物方程的边界可控性
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-04-06 DOI: 10.1007/s00498-024-00383-8
{"title":"Boundary controllability for a 1D degenerate parabolic equation with a Robin boundary condition","authors":"","doi":"10.1007/s00498-024-00383-8","DOIUrl":"https://doi.org/10.1007/s00498-024-00383-8","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we prove the null controllability of a one-dimensional degenerate parabolic equation with a weighted Robin boundary condition at the left endpoint, where the potential has a singularity. We use some results from the singular Sturm–Liouville theory to show the well-posedness of our system. We obtain a spectral decomposition of a degenerate parabolic operator with Robin conditions at the endpoints, we use Fourier–Dini expansions and the moment method introduced by Fattorini and Russell to prove the null controllability and to obtain an upper estimate of the cost of controllability. We also get a lower estimate of the cost of controllability by using a representation theorem for analytic functions of exponential type.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140596180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A two-player game representation for a class of infinite horizon control problems under state constraints 状态约束下一类无限视界控制问题的双人博弈表示法
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-03-16 DOI: 10.1007/s00498-024-00380-x
{"title":"A two-player game representation for a class of infinite horizon control problems under state constraints","authors":"","doi":"10.1007/s00498-024-00380-x","DOIUrl":"https://doi.org/10.1007/s00498-024-00380-x","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, feedback laws for a class of infinite horizon control problems under state constraints are investigated. We provide a two-player game representation for such control problems assuming time-dependent dynamics and Lagrangian and the set constraints merely compact. Using viability results recently investigated for state constrained problems in an infinite horizon setting, we extend some known results for the linear-quadratic regulator problem to a class of control problems with nonlinear dynamics in the state and affine in the control. Feedback laws are obtained under suitable controllability assumptions.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140149494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Averaging of a class of singularly perturbed control systems: a non-asymptotic result 一类奇异扰动控制系统的平均化：非渐近结果
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-03-13 DOI: 10.1007/s00498-024-00382-9
{"title":"Averaging of a class of singularly perturbed control systems: a non-asymptotic result","authors":"","doi":"10.1007/s00498-024-00382-9","DOIUrl":"https://doi.org/10.1007/s00498-024-00382-9","url":null,"abstract":"<h3>Abstract</h3> <p>We study a singularly perturbed control system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are dense in the set of solutions of a certain differential inclusion and discuss an implication of this result for optimal control.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"277 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Editorial to the collection of papers dedicated to Eduardo D. Sontag on the occasion of his 70th birthday 爱德华多-D.-桑塔格七十寿辰纪念论文集社论
IF 1.2 4区 计算机科学
Mathematics of Control Signals and Systems Pub Date : 2024-02-23 DOI: 10.1007/s00498-024-00381-w
Murat Arcak, Yacine Chitour, Patrick De Leenheer, Lars Grüne
{"title":"Editorial to the collection of papers dedicated to Eduardo D. Sontag on the occasion of his 70th birthday","authors":"Murat Arcak, Yacine Chitour, Patrick De Leenheer, Lars Grüne","doi":"10.1007/s00498-024-00381-w","DOIUrl":"https://doi.org/10.1007/s00498-024-00381-w","url":null,"abstract":"<p>This paper provides an editorial to the Collection of MCSS Papers dedicated to Eduardo D. Sontag on the occasion of his 70th birthday.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"33 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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