SIAM Journal on Control and Optimization最新文献

Local Exact Controllability of the One-Dimensional Nonlinear Schrödinger Equation in the Case of Dirichlet Boundary Conditions 迪里夏特边界条件情况下一维非线性薛定谔方程的局部精确可控性

IF 2.2 2区数学

SIAM Journal on Control and Optimization Pub Date : 2024-09-13 DOI: 10.1137/23m1556034

Alessandro Duca, Vahagn Nersesyan

{"title":"Local Exact Controllability of the One-Dimensional Nonlinear Schrödinger Equation in the Case of Dirichlet Boundary Conditions","authors":"Alessandro Duca, Vahagn Nersesyan","doi":"10.1137/23m1556034","DOIUrl":"https://doi.org/10.1137/23m1556034","url":null,"abstract":"SIAM Journal on Control and Optimization, Ahead of Print. <br/> Abstract. We consider the one-dimensional nonlinear Schrödinger equation with bilinear control. In the present paper, we study its local exact controllability near the ground state in the case of Dirichlet boundary conditions. To establish the controllability of the linearized equation, we use a bilinear control acting through four directions: three Fourier modes and one generic direction. The Fourier modes are appropriately chosen so that they satisfy a saturation property. These modes allow one to control approximately the linearzied Schrödinger equation. Then we show that the reachable set for the linearized equation is closed. This is achieved by representing the solution operator as a sum of two linear continuous mappings: one is surjective (here the control in generic direction is used) and the other is compact. A mapping with dense and closed image is surjective, so we conclude that the linearized Schrödinger equation is exactly controllable. The local exact controllability of the nonlinear equation then follows by the inverse mapping theorem.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Backward Stochastic Differential Equations with Conditional Reflection and Related Recursive Optimal Control Problems 带条件反射的后向随机微分方程及相关递归最优控制问题

IF 2.2 2区数学

SIAM Journal on Control and Optimization Pub Date : 2024-09-10 DOI: 10.1137/22m1534985

Ying Hu, Jianhui Huang, Wenqiang Li

{"title":"Backward Stochastic Differential Equations with Conditional Reflection and Related Recursive Optimal Control Problems","authors":"Ying Hu, Jianhui Huang, Wenqiang Li","doi":"10.1137/22m1534985","DOIUrl":"https://doi.org/10.1137/22m1534985","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 2557-2589, October 2024. <br/> Abstract. We introduce a new type of reflected backward stochastic differential equations (BSDEs) for which the reflection constraint is imposed on its main solution component, denoted as [math] by convention, but in terms of its conditional expectation [math] on a general subfiltration [math]. We thus term such a equation as conditionally reflected BSDE (for short, conditional RBSDE). Conditional RBSDE subsumes classical RBSDE with a pointwise reflection barrier and the recently developed BSDE with a mean reflection constraint as its two special and extreme cases: they exactly correspond to [math] being the full filtration to represent complete information and the degenerated filtration to deterministic scenario, respectively. For conditional RBSDE, we obtain its existence and uniqueness under mild conditions by combining the Snell envelope method with the Skorokhod lemma. We also discuss its connection, in the case of a linear driver, to a class of optimal stopping problems in the presence of partial information. As a by-product, a new version of the comparison theorem is obtained. With the help of this connection, we study weak formulations of a class of optimal control problems with reflected recursive functionals by characterizing the related optimal solution and value. Moreover, in the special case of recursive functionals being RBSDE with pointwise reflections, we study the strong formulations of related stochastic backward recursive control and zero-sum games, both in a non-Markovian framework, that are of their own interests and have not been fully explored by existing literature yet.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Ratcheting of Dividend Payout Under Brownian Motion Surplus 布朗运动盈余条件下的最优梯度股利分配

IF 2.2 2区数学

SIAM Journal on Control and Optimization Pub Date : 2024-09-10 DOI: 10.1137/23m159250x

Chonghu Guan, Zuo Quan Xu

{"title":"Optimal Ratcheting of Dividend Payout Under Brownian Motion Surplus","authors":"Chonghu Guan, Zuo Quan Xu","doi":"10.1137/23m159250x","DOIUrl":"https://doi.org/10.1137/23m159250x","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 2590-2620, October 2024. <br/> Abstract. This paper is concerned with a long-standing optimal dividend payout problem subject to the so-called ratcheting constraint, that is, the dividend payout rate shall be nondecreasing over time and is thus self-path-dependent. The surplus process is modeled by a drifted Brownian motion process and the aim is to find the optimal dividend ratcheting strategy to maximize the expectation of the total discounted dividend payouts until the ruin time. Due to the self-path-dependent control constraint, the standard control theory cannot be directly applied to tackle the problem. The related Hamilton–Jacobi–Bellman (HJB) equation is a new type of variational inequality. In the literature, it is only shown to have a viscosity solution, which is not strong enough to guarantee the existence of an optimal dividend ratcheting strategy. This paper proposes a novel partial differential equation method to study the HJB equation. We not only prove the existence and uniqueness of the solution in some stronger functional space, but also prove the strict monotonicity, boundedness, and [math]-smoothness of the dividend ratcheting free boundary. Based on these results, we eventually derive an optimal dividend ratcheting strategy, and thus solve the open problem completely. Economically speaking, we find that if the surplus volatility is above an explicit threshold, then one should pay dividends at the maximum rate, regardless of the surplus level. Otherwise, by contrast, the optimal dividend ratcheting strategy relies on the surplus level and one should only ratchet up the dividend payout rate when the surplus level touches the dividend ratcheting free boundary. Moreover, our numerical results suggest that one should invest in those companies with stable dividend payout strategies since their income rates should be higher and volatility rates smaller.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Logarithmic Regret Bounds for Continuous-Time Average-Reward Markov Decision Processes 连续时间平均回报马尔可夫决策过程的对数回归界线

IF 2.2 2区数学

SIAM Journal on Control and Optimization Pub Date : 2024-09-10 DOI: 10.1137/23m1584101

Xuefeng Gao, Xun Yu Zhou

引用次数: 0

An Optimal Spectral Inequality for Degenerate Operators 退化算子的最优谱不等式

IF 2.2 2区数学

SIAM Journal on Control and Optimization Pub Date : 2024-09-05 DOI: 10.1137/23m1605211

Rémi Buffe, Kim Dang Phung, Amine Slimani

引用次数: 0

A Tikhonov Theorem for McKean–Vlasov Two-Scale Systems and a New Application to Mean Field Optimal Control Problems 麦金-弗拉索夫双尺度系统的提霍诺夫定理及其在均值场最优控制问题中的新应用

IF 2.2 2区数学

SIAM Journal on Control and Optimization Pub Date : 2024-09-04 DOI: 10.1137/22m1543070

Matteo Burzoni, Alekos Cecchin, Andrea Cosso

引用次数: 0

Null Internal Controllability for a Kirchhoff–Love Plate with a Comb-Like Shaped Structure 具有梳齿状结构的基尔霍夫-洛夫板的无效内部可控性

IF 2.2 2区数学

SIAM Journal on Control and Optimization Pub Date : 2024-09-04 DOI: 10.1137/24m1647825

Umberto De Maio, Antonio Gaudiello, Cătălin-George Lefter

引用次数: 0

Stochastic Maximum Principle for Fully Coupled Forward-Backward Stochastic Differential Equations Driven by Subdiffusion 子扩散驱动的全耦合前后向随机微分方程的随机最大原则

IF 2.2 2区数学

SIAM Journal on Control and Optimization Pub Date : 2024-09-03 DOI: 10.1137/23m1620168

Shuaiqi Zhang, Zhen-Qing Chen

引用次数: 0

The Hybrid Maximum Principle for Optimal Control Problems with Spatially Heterogeneous Dynamics is a Consequence of a Pontryagin Maximum Principle for [math]-Local Solutions 空间异质动力学最优控制问题的混合最大原则是[数学]局部解的庞特里亚金最大原则的后果

IF 2.2 2区数学

SIAM Journal on Control and Optimization Pub Date : 2024-08-21 DOI: 10.1137/23m155311x

Térence Bayen, Anas Bouali, Loïc Bourdin

{"title":"The Hybrid Maximum Principle for Optimal Control Problems with Spatially Heterogeneous Dynamics is a Consequence of a Pontryagin Maximum Principle for [math]-Local Solutions","authors":"Térence Bayen, Anas Bouali, Loïc Bourdin","doi":"10.1137/23m155311x","DOIUrl":"https://doi.org/10.1137/23m155311x","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 2412-2432, August 2024. <br/> Abstract. The title of the present work is a nod to the paper “The hybrid maximum principle is a consequence of Pontryagin maximum principle” by Dmitruk and Kaganovich [Systems Control Lett., 57 (2008), pp. 964–970]. We investigate a similar framework of hybrid optimal control problems that is also different from Dmitruk and Kaganovich’s. Precisely, we consider a general control system that is described by a differential equation involving a spatially heterogeneous dynamics. In that context, the sequence of dynamics followed by the trajectory and the corresponding switching times are fully constrained by the state position. We prove with an explicit counterexample that the augmentation technique used by Dmitruk and Kaganovich cannot be fully applied to our setting, but we show that it can be adapted by introducing a new notion of local solution to classical optimal control problems and by establishing a corresponding Pontryagin maximum principle. Thanks to this method, we derive a hybrid maximum principle adapted to our setting, with a simple proof that does not require any technical tools (such as implicit function arguments) to handle the dynamical discontinuities.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Chain Controllability of Linear Control Systems 线性控制系统的连锁可控性

IF 2.2 2区数学

SIAM Journal on Control and Optimization Pub Date : 2024-08-19 DOI: 10.1137/23m1626347

Fritz Colonius, Alexandre J. Santana, Eduardo C. Viscovini

引用次数: 0