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Improved error estimates for optimal control of the Stokes problem with pointwise tracking in three dimensions 三维点跟踪Stokes问题最优控制的改进误差估计
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI: 10.3934/mcrf.2020038
Niklas Behringer
{"title":"Improved error estimates for optimal control of the Stokes problem with pointwise tracking in three dimensions","authors":"Niklas Behringer","doi":"10.3934/mcrf.2020038","DOIUrl":"https://doi.org/10.3934/mcrf.2020038","url":null,"abstract":". This work is motivated by recent interest in the topic of pointwise tracking type optimal control problems for the Stokes problem. Pointwise tracking consists of point evaluations in the objective functional which lead to Dirac measures appearing as source terms of the adjoint problem. Consider- ing bounds for the control allows for improved regularity results for the exact solution and improved approximation error estimates of its numerical coun- terpart. We show a sub-optimal convergence result in three dimensions that nonetheless improves the results known from the literature. Finally, we offer supporting numerical experiments and insights towards optimal approximation error estimates.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74818296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A tracking problem for the state of charge in a electrochemical Li-ion battery model 电化学锂离子电池模型中电荷状态的跟踪问题
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI: 10.3934/mcrf.2021041
Esteban Hernández, C. Prieur, Eduardo Cerpa
{"title":"A tracking problem for the state of charge in a electrochemical Li-ion battery model","authors":"Esteban Hernández, C. Prieur, Eduardo Cerpa","doi":"10.3934/mcrf.2021041","DOIUrl":"https://doi.org/10.3934/mcrf.2021041","url":null,"abstract":"In this paper the Single Particle Model is used to describe the behavior of a Li-ion battery. The main goal is to design a feedback input current in order to regulate the State of Charge (SOC) to a prescribed reference trajectory. In order to do that, we use the boundary ion concentration as output. First, we measure it directly and then we assume the existence of an appropriate estimator, which has been established in the literature using voltage measurements. By applying backstepping and Lyapunov tools, we are able to build observers and to design output feedback controllers giving a positive answer to the SOC tracking problem. We provide convergence proofs and perform some numerical simulations to illustrate our theoretical results.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72415126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities 输入非线性的多变量线性无穷维系统的采样数据积分控制
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI: 10.3934/MCRF.2021001
Max E. Gilmore, C. Guiver, H. Logemann
{"title":"Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities","authors":"Max E. Gilmore, C. Guiver, H. Logemann","doi":"10.3934/MCRF.2021001","DOIUrl":"https://doi.org/10.3934/MCRF.2021001","url":null,"abstract":"A low-gain integral controller with anti-windup component is presented for exponentially stable, linear, discrete-time, infinite-dimensional control systems subject to input nonlinearities and external disturbances. We derive a disturbance-to-state stability result which, in particular, guarantees that the tracking error converges to zero in the absence of disturbances. The discrete-time result is then used in the context of sampled-data low-gain integral control of stable well-posed linear infinite-dimensional systems with input nonlinearities. The sampled-date control scheme is applied to two examples (including sampled-data control of a heat equation on a square) which are discussed in some detail.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90529968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Error-based control systems on Riemannian state manifolds: Properties of the principal pushforward map associated to parallel transport 黎曼状态流形上基于误差的控制系统:与并行传输相关的主前推映射的性质
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI: 10.3934/mcrf.2020031
S. Fiori
{"title":"Error-based control systems on Riemannian state manifolds: Properties of the principal pushforward map associated to parallel transport","authors":"S. Fiori","doi":"10.3934/mcrf.2020031","DOIUrl":"https://doi.org/10.3934/mcrf.2020031","url":null,"abstract":"The objective of the paper is to contribute to the theory of error-based control systems on Riemannian manifolds. The present study focuses on system where the control field influences the covariant derivative of a control path. In order to define error terms in such systems, it is necessary to compare tangent vectors at different points using parallel transport and to understand how the covariant derivative of a vector field along a path changes after such field gets parallely transported to a different curve. It turns out that such analysis relies on a specific map, termed principal pushforward map. The present paper aims at contributing to the algebraic theory of the principal pushforward map and of its relationship with the curvature endomorphism of a state manifold.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75962407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Optimal control of transverse vibration of a moving string with time-varying lengths 时变运动弦横向振动的最优控制
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI: 10.3934/mcrf.2021042
Bing Sun
{"title":"Optimal control of transverse vibration of a moving string with time-varying lengths","authors":"Bing Sun","doi":"10.3934/mcrf.2021042","DOIUrl":"https://doi.org/10.3934/mcrf.2021042","url":null,"abstract":"In this article, we are concerned with optimal control for the transverse vibration of a moving string with time-varying lengths. In the fixed final time horizon case, the Pontryagin maximum principle is established for the investigational system with a moving boundary, owing to the Dubovitskii and Milyutin functional analytical approach. A remark then follows for discussing the utilization of obtained necessary optimality condition.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78654065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal dividend policy in an insurance company with contagious arrivals of claims 具有传染性索赔到达的保险公司的最优股利政策
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI: 10.3934/mcrf.2020024
Yiling Chen, B. Bian
{"title":"Optimal dividend policy in an insurance company with contagious arrivals of claims","authors":"Yiling Chen, B. Bian","doi":"10.3934/mcrf.2020024","DOIUrl":"https://doi.org/10.3934/mcrf.2020024","url":null,"abstract":"In this paper we consider the optimal dividend problem for an insurance company whose surplus follows a classical Cramer-Lundberg process with a feature of self-exciting. A Hawkes process is applied so that the occurrence of a jump in the claims triggers more sequent jumps. We show that the optimal value function is a unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation with a given boundary condition and declare its concavity. We introduce a barrier curve strategy and verify its optimality. Finally, some numerical results are exhibited.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83856345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A nonlinear version of Halanay's inequality for the uniform convergence to the origin 一致收敛到原点的哈拉奈不等式的一个非线性版本
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI: 10.3934/mcrf.2021045
P. Pepe
{"title":"A nonlinear version of Halanay's inequality for the uniform convergence to the origin","authors":"P. Pepe","doi":"10.3934/mcrf.2021045","DOIUrl":"https://doi.org/10.3934/mcrf.2021045","url":null,"abstract":"A nonlinear version of Halanay's inequality is studied in this paper as a sufficient condition for the convergence of functions to the origin, uniformly with respect to bounded sets of initial values. The same result is provided in the case of forcing terms, for the uniform convergence to suitable neighborhoods of the origin. Related Lyapunov methods for the global uniform asymptotic stability and the input-to-state stability of systems described by retarded functional differential equations, with possibly nonconstant time delays, are provided. The relationship with the Razumikhin methodology is shown.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77371362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Second order directional shape derivatives of integrals on submanifolds 子流形上积分的二阶方向形状导数
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI: 10.3934/MCRF.2021017
A. Schiela, Julian Ortiz
{"title":"Second order directional shape derivatives of integrals on submanifolds","authors":"A. Schiela, Julian Ortiz","doi":"10.3934/MCRF.2021017","DOIUrl":"https://doi.org/10.3934/MCRF.2021017","url":null,"abstract":"We compute first and second order shape sensitivities of integrals on smooth submanifolds using a variant of shape differentiation. The result is a quadratic form in terms of one perturbation vector field that yields a second order quadratic model of the perturbed functional. We discuss the structure of this derivative, derive domain expressions and Hadamard forms in a general geometric framework, and give a detailed geometric interpretation of the arising terms.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74753140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
General decay and blow-up for coupled Kirchhoff wave equations with dynamic boundary conditions 具有动态边界条件的耦合Kirchhoff波动方程的一般衰减和爆破
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI: 10.3934/mcrf.2021058
Meng Lv, Jianghao Hao
{"title":"General decay and blow-up for coupled Kirchhoff wave equations with dynamic boundary conditions","authors":"Meng Lv, Jianghao Hao","doi":"10.3934/mcrf.2021058","DOIUrl":"https://doi.org/10.3934/mcrf.2021058","url":null,"abstract":"<p style='text-indent:20px;'>In this paper we consider a system of viscoelastic wave equations of Kirchhoff type with dynamic boundary conditions. Supposing the relaxation functions <inline-formula><tex-math id=\"M1\">begin{document}$ g_i $end{document}</tex-math></inline-formula> <inline-formula><tex-math id=\"M2\">begin{document}$ (i = 1, 2, cdots, l) $end{document}</tex-math></inline-formula> satisfy <inline-formula><tex-math id=\"M3\">begin{document}$ g_i(t)leq-xi_i(t)G(g_i(t)) $end{document}</tex-math></inline-formula> where <inline-formula><tex-math id=\"M4\">begin{document}$ G $end{document}</tex-math></inline-formula> is an increasing and convex function near the origin and <inline-formula><tex-math id=\"M5\">begin{document}$ xi_i $end{document}</tex-math></inline-formula> are nonincreasing, we establish some optimal and general decay rates of the energy using the multiplier method and some properties of convex functions. Moreover, we obtain the finite time blow-up result of solution with nonpositive or arbitrary positive initial energy. The results in this paper are obtained without imposing any growth condition on weak damping term at the origin. Our results improve and generalize several earlier related results in the literature.</p>","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83281249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Local Kalman rank condition for linear time varying systems 线性时变系统的局部卡尔曼秩条件
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI: 10.3934/MCRF.2021029
H. Maarouf
{"title":"Local Kalman rank condition for linear time varying systems","authors":"H. Maarouf","doi":"10.3934/MCRF.2021029","DOIUrl":"https://doi.org/10.3934/MCRF.2021029","url":null,"abstract":"In this paper, we study some non-negative integers related to a linear time varying system and to some Krylov sub-spaces associated to this system. Such integers are similar to the controllability indices and have been used in the literature to derive results on the controllability of linear systems. The purpose of this paper goes in the same direction by studying the local behavior of these integers especially nearby instants in the time interval with some maximal rank condition and then apply them to get some results which generalize the mentioned existing results.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82707711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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