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Esaim-Control Optimisation and Calculus of Variations最新文献

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Goh conditions for minima of nonsmooth control problems 非光滑控制问题的两个最小值条件
IF 1.4 3区 数学
Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-03 DOI: 10.1051/cocv/2023003
Francesca Angrisani, F. Rampazzo
{"title":"Goh conditions for minima of nonsmooth control problems","authors":"Francesca Angrisani, F. Rampazzo","doi":"10.1051/cocv/2023003","DOIUrl":"https://doi.org/10.1051/cocv/2023003","url":null,"abstract":"Les conditions nécessaires d'ordre supérieur pour un minimiseur d'un problème de contrôle optimal sont généralement obtenues pour des systèmes dont la dynamique est $C^1$ en la variable d'état. Ici, en utilisant la notion de crochet de Lie multivoque, nous obtenons une condition de type Goh pour un système de contrôle affine avec une dynamique Lipschitz et des contrôles non bornés. Afin de gérer le manque de régularité simultané de l'équation adjointe et des variations de type crochet de Lie, nous utilisons la notion de Quasi Differential Quotient.  Nous concluons le papier avec un exemple qui montre comment la condition d'ordre supérieur établie permet d'exclure l'optimalité d'un contrôle vérifiant le principe du maximum classique.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78612918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Controllability and observability for some forward stochastic complex degenerate/singular Ginzburg-Landau equations                   一类正向随机复退化/奇异金兹堡-朗道方程的可控性和可观测性
IF 1.4 3区 数学
Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-03 DOI: 10.1051/cocv/2023002
Yongyi Yu, Qingmei Zhao
{"title":"Controllability and observability for some forward stochastic complex degenerate/singular Ginzburg-Landau equations\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 ","authors":"Yongyi Yu, Qingmei Zhao","doi":"10.1051/cocv/2023002","DOIUrl":"https://doi.org/10.1051/cocv/2023002","url":null,"abstract":"This  paper is addressed to establishing controllability and observability for some forward stochastic complex degenerate/singular Ginzburg-Landau equations. It is sufficient to establish appropriate observability inequalities for the corresponding backward and forward equations. The key is to prove the Carleman estimates of the forward and backward stochastic complex degenerate/singular Ginzburg-Landau operators. Compared with the existing deterministic results, it is necessary to overcome the difficulties caused by some complex coefficients and random terms. The results obtained cover those of deterministic cases and generalize those of stochastic degenerate parabolic equations. Moreover, the limit behavior of the coefficients in\u0000the equation is discussed.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87050513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Class of One Dimensional Periodic Microstructures Exhibiting Effective Timoshenko Beam Behavior 一类具有有效Timoshenko束行为的一维周期微结构
IF 1.4 3区 数学
Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-01 DOI: 10.1051/cocv/2023048
J. Alibert, E. Barchiesi, F. dell’Isola, P. Seppecher
{"title":"A Class of One Dimensional Periodic Microstructures Exhibiting Effective Timoshenko Beam Behavior","authors":"J. Alibert, E. Barchiesi, F. dell’Isola, P. Seppecher","doi":"10.1051/cocv/2023048","DOIUrl":"https://doi.org/10.1051/cocv/2023048","url":null,"abstract":"We study, from a variational viewpoint, the asymptotic behavior of a planar beam with a periodic wavy shape when the amplitude and the wavelength of the shape tend to zero. We assume that the beam behaves, at the microscopic level, as a compressible Euler–Bernoulli beam and that the material properties have the same period as the geometry. We allow for distributed or concentrated bending compliance and for a non-quadratic extensional energy. The macroscopic Γ-limit that we obtain corresponds to a non-linear model of Timoshenko type.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77009379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Well-posedness and regularity for a polyconvex energy 多凸能量的适位性和正则性
3区 数学
Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-01 DOI: 10.1051/cocv/2023041
Wilfrid Gangbo, Matt Jacobs, Inwon Kim
{"title":"Well-posedness and regularity for a polyconvex energy","authors":"Wilfrid Gangbo, Matt Jacobs, Inwon Kim","doi":"10.1051/cocv/2023041","DOIUrl":"https://doi.org/10.1051/cocv/2023041","url":null,"abstract":"We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional in two and three dimensions, which corresponds to the $H^1$ projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. As an application, we construct a minimizing movement scheme to construct $L^r$ solutions of the Navier-Stokes equation for a short time interval.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
An exit contract optimization problem 一个退出契约优化问题
3区 数学
Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-01 DOI: 10.1051/cocv/2023064
Xihao He, Xiaolu Tan, Jun Zou
{"title":"An exit contract optimization problem","authors":"Xihao He, Xiaolu Tan, Jun Zou","doi":"10.1051/cocv/2023064","DOIUrl":"https://doi.org/10.1051/cocv/2023064","url":null,"abstract":"We study an exit contract design problem, where one provides a universal exit contract to multiple heterogeneous agents, with which each agent chooses an optimal (exit) stopping time. The problem consists in optimizing the universal exit contract w.r.t. some criterion depending on the contract as well as the agents’ exit times. Under a technical monotonicity condition, and by using Bank-El Karoui’s representation of stochastic processes, we are able to transform the initial contract optimization problem into an optimal control problem. The latter is also equivalent to an optimal multiple stopping problem and the existence of the optimal contract is proved. We next show that the problem in the continuous-time setting can be approximated by a sequence of discrete-time ones, which would induce a natural numerical approximation method. We finally discuss the optimization problem over the class of all Markovian and/or continuous exit contracts.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135445778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Variational problems in involving semilinear second order differential operators p, li { white-space: pre-wrap; } 半线性二阶微分算子p, li{的变分问题｝
3区 数学
Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-01 DOI: 10.1051/cocv/2023066
Nikos Katzourakis, Roger Moser
{"title":"Variational problems in involving semilinear second order differential operators p, li { white-space: pre-wrap; }","authors":"Nikos Katzourakis, Roger Moser","doi":"10.1051/cocv/2023066","DOIUrl":"https://doi.org/10.1051/cocv/2023066","url":null,"abstract":"For an elliptic, semilinear differential operator of the form S ( u ) = A : D 2 u + b ( x , u , Du ), consider the functional E ∞ ( u ) = ess sup Ω , | S ( u )|. We study minimisers of E ∞ for prescribed boundary data. Because the functional is not differentiable, this problem does not give rise to a conventional Euler-Lagrange equation. Under certain conditions, we can nevertheless give a system of partial differential equations that all minimisers must satisfy. Moreover, the condition is equivalent to a weaker version of the variational problem. The theory of partial differential equations therefore becomes available for the study of a large class of variational problems in L ∞ for the first time.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135500833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Saturated boundary feedback control of quasi-linear hyperbolic balance laws with application to LWR traffic flow stabilization 准线性双曲平衡律的饱和边界反馈控制及其在轻水车交通流稳定中的应用
3区 数学
Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-01 DOI: 10.1051/cocv/2023070
Hanxu Zhao, Jingyuan Zhan, Liguo Zhang
{"title":"Saturated boundary feedback control of quasi-linear hyperbolic balance laws with application to LWR traffic flow stabilization","authors":"Hanxu Zhao, Jingyuan Zhan, Liguo Zhang","doi":"10.1051/cocv/2023070","DOIUrl":"https://doi.org/10.1051/cocv/2023070","url":null,"abstract":"The saturated boundary stabilization problem for quasi-linear hyperbolic systems of balance laws is considered under H 2 -norm in this paper, where the boundary conditions of the system are subject to actuator saturations. The resulting closed-loop system is proven to be locally exponentially stable with respect to the steady states in the presence of saturations. To this end, the sector nonlinearity model is introduced to deal with the saturation term, and then sufficient conditions for ensuring the locally exponential stability are established in terms of a set of matrix inequalities by employing the Lyapunov function method along with a sector condition. Furthermore, these results are applied to the stabilization of the two-lane traffic flow dynamic represented by Lighthill–Whitham–Richards (LWR) model. By utilizing variable speed limit (VSL) devices, a saturated boundary feedback controller is designed to stabilize the two-lane traffic flow, and the exponential convergence of the quasi-linear traffic flow system in H 2 sense is validated by numerical simulations.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135799102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Stability of inverse source problem for a transmission wave equation with multiple interfaces of discontinuity 具有多个不连续界面的透射波方程反源问题的稳定性
IF 1.4 3区 数学
Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-01 DOI: 10.1051/cocv/2023031
Zifan Jiang, Wensheng Zhang
{"title":"Stability of inverse source problem for a transmission wave equation with multiple interfaces of discontinuity","authors":"Zifan Jiang, Wensheng Zhang","doi":"10.1051/cocv/2023031","DOIUrl":"https://doi.org/10.1051/cocv/2023031","url":null,"abstract":"In this paper, we consider a transmission wave equation in N embedded domains with multiple interfaces of discontinuous coefficients in ℝ2. We study the global stability in determining the source term from a one-measurement data of wavefield velocity in a subboundary over a time interval. We prove the stability estimate for this inverse source problem by a combination of the local hyperbolic/elliptic Carleman estimates and the Fourier-Bros-Iagolniter transformation. Our method could be generalized to general dimensions since the weight functions and Carleman estimates are independent of the dimensions.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85612460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Surfaces of genus g≥ 1 in 3D contact sub-Riemannian manifolds 三维接触亚黎曼流形中g属≥1的曲面
3区 数学
Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-01 DOI: 10.1051/cocv/2023072
Eugenio Bellini, Ugo Boscain
{"title":"Surfaces of genus g≥ 1 in 3D contact sub-Riemannian manifolds","authors":"Eugenio Bellini, Ugo Boscain","doi":"10.1051/cocv/2023072","DOIUrl":"https://doi.org/10.1051/cocv/2023072","url":null,"abstract":"We consider smooth embedded surfaces in a 3D contact sub-Riemannian manifold and the problem of the finiteness of the induced distance ( i.e. , the infimum of the length of horizontal curves that belong to the surface). Recently it has been proved that for a surface having the topology of a sphere embedded in a tight co-orientable structure, the distance is always finite. In this paper we study closed surfaces of genus larger than 1, proving that such surfaces can be embedded in such a way that the induced distance is finite or infinite. We then study the structural stability of the fmiteness/not-finiteness of the distance.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135910636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Rates of convergence in periodic homogenization of nonlocal Hamilton–Jacobi–Bellman equations, 非局部Hamilton-Jacobi-Bellman方程周期均匀化的收敛速率
3区 数学
Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-01 DOI: 10.1051/cocv/2023038
Andrei Rodríguez-Paredes, Erwin Topp
{"title":"Rates of convergence in periodic homogenization of nonlocal Hamilton–Jacobi–Bellman equations,","authors":"Andrei Rodríguez-Paredes, Erwin Topp","doi":"10.1051/cocv/2023038","DOIUrl":"https://doi.org/10.1051/cocv/2023038","url":null,"abstract":"In this paper we provide a rate of convergence for periodic homogenization of Hamilton–Jacobi–Bellman equations with nonlocal diffusion. The result is based on the regularity of the associated effective problem, where convexity plays a crucial role. The necessary regularity estimates are made possible by a representation formula we obtain for the effective Hamiltonian, a result that has an independent interest.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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