Mathematical Control and Related Fields最新文献_第4页

Optimal control of a global model of climate change with adaptation and mitigation 具有适应和减缓的全球气候变化模式的最优控制

4区数学

Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI: 10.3934/mcrf.2022009

Manoj Atolia, Prakash Loungani, Helmut Maurer, Willi Semmler

{"title":"Optimal control of a global model of climate change with adaptation and mitigation","authors":"Manoj Atolia, Prakash Loungani, Helmut Maurer, Willi Semmler","doi":"10.3934/mcrf.2022009","DOIUrl":"https://doi.org/10.3934/mcrf.2022009","url":null,"abstract":"The economy-climate interaction and an appropriate mitigation policy for climate protection have been treated in various types of scientific modeling. Here, we specifically focus on the seminal work by Nordhaus [14, 15] on the economy-climate link. We extend the Nordhaus type model to include optimal policies for mitigation, adaptation and infrastructure investment studying the dynamics of the transition to a low fossil-fuel economy. Formally, the model gives rise to an optimal control problem consisting of a dynamic system with five-dimensional state vector representing stocks of private capital, green capital, public capital, stock of brown energy in the ground, and carbon emissions. The objective function captures preferences over consumption but is also impacted by atmospheric $ mathrm{CO}_2 $ and by mitigation and adaptation policies. Given the numerous challenges to climate change policies the control vector is eight-dimensional comprising mitigation, adaptation and infrastructure investment. Our solutions are characterized by turnpike property and the optimal policies that accomplish the objective of keeping the $ mathrm{CO}_2 $ levels within bound are characterized by a significant proportion of investment in public capital going to mitigation in the initial periods. When initial levels of $ mathrm{CO}_{2} $ are high, adaptation efforts also start immediately, but during the initial period, they account for a smaller proportion of government's public investment.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136297316","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

Value functional and optimal feedback control in linear-quadratic optimal control problem for fractional-order system 分数阶系统线性二次最优控制问题中的值泛函与最优反馈控制

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-08-30 DOI: 10.3934/mcrf.2023002

M. Gomoyunov

引用次数: 2

Moment stability of stochastic processes with applications to control systems 随机过程的矩稳定性及其在控制系统中的应用

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-06-01 DOI: 10.3934/mcrf.2023008

A. Ganguly, D. Chatterjee

引用次数: 0

On the new coupled complex boundary method in shape optimization framework for solving stationary free boundary problems 形状优化框架中求解平稳自由边界问题的新耦合复边界法

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-05-25 DOI: 10.3934/mcrf.2022041

J. F. Rabago

{"title":"On the new coupled complex boundary method in shape optimization framework for solving stationary free boundary problems","authors":"J. F. Rabago","doi":"10.3934/mcrf.2022041","DOIUrl":"https://doi.org/10.3934/mcrf.2022041","url":null,"abstract":"We expose here a novel application of the so-called coupled complex boundary method – first put forward by Cheng et al. (2014) to deal with inverse source problems – in the framework of shape optimization for solving the exterior Bernoulli problem, a prototypical model of stationary free boundary problems. The idea of the method is to transform the overdetermined problem to a complex boundary value problem with a complex Robin boundary condition coupling the Dirichlet and Neumann boundary conditions on the free boundary. Then, we optimize the cost function constructed by the imaginary part of the solution in the whole domain in order to identify the free boundary. We also prove the existence of the shape derivative of the complex state with respect to the domain. Afterwards, we compute the shape gradient of the cost functional, and characterize its shape Hessian at the optimal domain under a strong, and then a mild regularity assumption on the domain. We then prove the ill-posedness of the proposed shape problem by showing that the latter expression is compact. Also, we devise an iterative algorithm based on a Sobolev gradient scheme via finite element method to solve the minimization problem. Finally, we illustrate the applicability of the method through several numerical examples, both in two and three spatial dimensions.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"39 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73829923","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: 4

Robust controllers for a flexible satellite model 柔性卫星模型的鲁棒控制器

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-04-07 DOI: 10.3934/mcrf.2023007

T. Govindaraj, Jukka-Pekka Humaloja, L. Paunonen

引用次数: 1

Numerical boundary control for semilinear hyperbolic systems 半线性双曲系统的数值边界控制

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-03-28 DOI: 10.3934/mcrf.2022040

Stephan Gerster, F. Nagel, Aleksey Sikstel, G. Visconti

引用次数: 0

Optimal control of a nonsmooth PDE arising in the modeling of shear–thickening fluids 剪切增稠流体建模中出现的非光滑偏微分方程的最优控制

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-03-06 DOI: 10.3934/mcrf.2023009

J. C. Reyes, Paola Quiloango

引用次数: 0

Impulse null approximate controllability for heat equation with dynamic boundary conditions 具有动态边界条件的热方程的脉冲零近似可控性

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-02-28 DOI: 10.3934/mcrf.2022026

Salah-Eddine Chorfi, G. E. Guermai, L. Maniar, W. Zouhair

引用次数: 3

Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies 用两个实例说明了最优控制中异常测地线的可达性

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-02-23 DOI: 10.3934/mcrf.2022052

B. Bonnard, J. Rouot, B. Wembe

{"title":"Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies","authors":"B. Bonnard, J. Rouot, B. Wembe","doi":"10.3934/mcrf.2022052","DOIUrl":"https://doi.org/10.3934/mcrf.2022052","url":null,"abstract":"In this article, we use two case studies from geometry and optimal control of chemical network to analyze the relation between abnormal geodesics in time optimal control, accessibility properties and regularity of the time minimal value function. Introduction. In this article, one considers the time minimal control problem for a smooth system of the form dq dt = f(q, u), where q ∈ M is an open subset of R n and the set of admissible control is the set U of bounded measurable mapping u(·) valued in a control domain U , where U is a two-dimensional manifold of R with boundary. According to the Maximum Principle [14], time minimal solutions are extremal curves satisfying the constrained Hamiltonian equation q̇ = ∂H ∂p , ṗ = − ∂q , H(q, p, u) = M(q, p), (1) where H(q, p, u) = p ·F (q, u) is the pseudo (or non maximized) Hamiltonian, while M(q, p) = maxv∈U H(q, p, u) is the true (maximized) Hamiltonian. A projection of an extremal curve z = (q, p) on the q-space is called a geodesic. Moreover since M is constant along an extremal curve and linear with respect to p, the extremal can be either exceptional (abnormal) if M = 0 or non exceptional if M 6= 0. To refine this classification, an extremal subarc can be either regular if the control belongs to the boundary of U or singular if it belongs to the interior and satisfies the condition ∂H ∂u = 0. Taking q(0) = q0 the accessibility set A(q0, tf ) in time tf is the set ∪u(·)∈U q(tf , x0, u), where t 7→ q(·, q0, u) denotes the solution of the system, with q(0) = q0 and clearly since the time minimal trajectories belongs to the boundary of the accessibility set, the Maximum Principle is a parameterization of this boundary. 2020 Mathematics Subject Classification. Primary: 49K15, 49L99, 53C60, 58K50.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"4 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73515743","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

Quantitative unique continuation for parabolic equations with Neumann boundary conditions 具有Neumann边界条件的抛物方程的定量唯一延拓

IF 1.2 4区数学

Mathematical Control and Related Fields Pub Date : 2022-02-21 DOI: 10.3934/mcrf.2022058

Yueliang Duan, Lijuan Wang, Can Zhang

引用次数: 1