SIAM Journal on Control and Optimization最新文献

英文中文

Minimal Control Placement of Networked Reaction-Diffusion Systems Based on Turing Model 基于图灵模型的网络反应扩散系统的最小控制布局

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization

Pub Date : 2024-06-24 DOI: 10.1137/23m1616856

Yuexin Cao, Yibei Li, Lirong Zheng, Xiaoming Hu

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1809-1831, June 2024.
Abstract. In this paper, we consider the problem of placing a minimal number of controls to achieve controllability for a class of networked control systems that are based on the original Turing reaction-diffusion model, which is governed by a set of ordinary differential equations with interactions defined by a ring graph. Turing model considers two morphogens reacting and diffusing over the spatial domain and has been widely accepted as one of the most fundamental models to explain pattern formation in a developing embryo. It is of great importance to understand the mechanism behind the various reaction kinetics that generate such a wide range of patterns. As a first step towards this goal, in this paper we study controllability of Turing model for the case of cells connected as a square grid in which controls can be applied to the boundary cells. We first investigate the minimal control placement problem for the diffusion only system. The eigenvalues of the diffusion matrix are classified by their geometric multiplicity, and the properties of the corresponding eigenspaces are studied. The symmetric control sets are designed to categorize control candidates by symmetry of the network topology. Then the necessary and sufficient condition is provided for placing the minimal control to guarantee controllability for the diffusion system. Furthermore, we show that the necessary condition can be extended to Turing model by a natural expansion of the symmetric control sets. Under certain circumstances, we prove that it is also sufficient to ensure controllability of Turing model.

SIAM 控制与优化期刊》第 62 卷第 3 期第 1809-1831 页，2024 年 6 月。摘要图灵反应-扩散模型由一组常微分方程控制，其相互作用由环形图定义。图灵模型考虑了两种形态发生反应并在空间域扩散的情况，被广泛认为是解释发育中胚胎模式形成的最基本模型之一。了解产生如此广泛模式的各种反应动力学背后的机制非常重要。作为实现这一目标的第一步，我们在本文中研究了图灵模型的可控性，即细胞连接成方形网格的情况，其中可对边界细胞施加控制。我们首先研究了仅扩散系统的最小控制位置问题。根据几何多重性对扩散矩阵的特征值进行分类，并研究相应特征空间的特性。设计了对称控制集，根据网络拓扑的对称性对控制候选集进行分类。然后提供了放置最小控制以保证扩散系统可控性的必要条件和充分条件。此外，我们还证明了必要条件可以通过对称控制集的自然扩展扩展到图灵模型。在某些情况下，我们证明这也足以保证图灵模型的可控性。

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引用次数: 0

Flatness Approach for the Boundary Controllability of a System of Heat Equations 热方程组边界可控性的平整度方法

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization

Pub Date : 2024-06-19 DOI: 10.1137/23m1577833

Blaise Colle, Jérôme Lohéac, Takéo Takahashi

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1766-1782, June 2024.
Abstract. We study the boundary controllability of [math] system of heat equations by using a flatness approach. According to the relation between the diffusion coefficients of the heat equation, it is known that the system can be neither null-controllable nor null-controllable for any [math], where [math]. Here we recover this result in the case that [math] by using the flatness method, and we obtain an explicit formula for the control and for the corresponding solutions. In particular, the state and the control have Gevrey regularity in time and in space.

SIAM 控制与优化期刊》第 62 卷第 3 期第 1766-1782 页，2024 年 6 月。摘要。我们用平整度方法研究了[math]热方程组的边界可控性。根据热方程扩散系数之间的关系可知，对于任意[math]，其中[math]，系统既不可能是空可控的，也不可能是空可控的。在这里，我们通过平差法在 [math] 的情况下恢复了这一结果，并得到了控制和相应解的显式。特别是，状态和控制在时间和空间上都具有 Gevrey 正则性。

引用次数: 0

Nonconservative Stability Criteria for Semi-Markovian Impulsive Switched Systems 半马尔可夫冲动开关系统的非保守稳定标准

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization

Pub Date : 2024-06-19 DOI: 10.1137/23m1564833

Shenyu Liu, Penghui Wen

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1783-1808, June 2024.
Abstract. This paper proposes criteria for establishing the asymptotic moment stability of semi-Markovian impulsive switched systems. Under some mild assumptions, we formulate an auxiliary linear time-delayed system based on the Lyapunov characterizations of the subsystems and impulses, as well as the properties of the underlying semi-Markovian impulsive switching signal. Our main result provides an upper bound on the moment, which is directly related to a solution of the aforementioned linear time-delayed system. Specifically, the semi-Markovian impulsive switched system is asymptotically moment stable if the auxiliary linear time-delayed system is asymptotically stable. In situations where the mode-dependent sojourn time distributions of the underlying impulsive switching signals are all exponential, uniform, or trigonometric, we deduce explicit formulae for the auxiliary linear time-delayed systems. To prove the main result, we compute the expected gain function, which requires formulating a generalized renewal equation. Finally, we test our stability criteria on a numerical example in different scenarios and show that our stability results are nonconservative compared to the statistically obtained average of state-norms and state-norm-squares.

SIAM 控制与优化期刊》第 62 卷第 3 期第 1783-1808 页，2024 年 6 月。摘要本文提出了建立半马尔可夫冲动开关系统渐近矩稳定性的准则。在一些温和的假设条件下，我们基于子系统和脉冲的 Lyapunov 特性以及底层半马尔可夫脉冲切换信号的特性，提出了一个辅助线性延时系统。我们的主要结果提供了矩的上界，它与上述线性延时系统的解直接相关。具体来说，如果辅助线性延时系统是渐近稳定的，那么半马尔可夫脉冲切换系统就是渐近矩稳定的。在底层脉冲切换信号的与模式相关的停留时间分布都是指数分布、均匀分布或三角分布的情况下，我们推导出了辅助线性延时系统的显式。为了证明主要结果，我们计算了预期增益函数，这需要提出一个广义更新方程。最后，我们在不同场景下的一个数值示例中测试了我们的稳定性标准，结果表明，与统计得出的状态正态和状态正态平方的平均值相比，我们的稳定性结果并不保守。

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引用次数: 0

Mean Field Games in a Stackelberg Problem with an Informed Major Player 有知情大玩家的堆叠尔伯格问题中的均场博弈

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization

Pub Date : 2024-06-13 DOI: 10.1137/23m1615188

Philippe Bergault, Pierre Cardaliaguet, Catherine Rainer

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1737-1765, June 2024.
Abstract. We investigate a stochastic differential game in which a major player has private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash mean field game equilibrium. The major player’s cost depends on the distribution of the population, while the cost of the population depends on the random variable known by the major player. We show that the game has a relaxed solution and that the optimal control of the major player is approximatively optimal in games with a large but finite number of small players.

SIAM 控制与优化期刊》第 62 卷第 3 期第 1737-1765 页，2024 年 6 月。摘要。我们研究了一个随机微分博弈，在这个博弈中，主要博弈者拥有私人信息（随机变量的知识），她通过控制权将这些信息透露给在纳什均场博弈均衡中博弈的小博弈者群体。主要玩家的成本取决于群体的分布，而群体的成本则取决于主要玩家已知的随机变量。我们证明了博弈有一个松弛解，而且在小博弈者数量众多但有限的博弈中，主要博弈者的最优控制近似最优。

引用次数: 0

The Occupation Kernel Method for Nonlinear System Identification 用于非线性系统识别的占位核方法

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization

Pub Date : 2024-06-11 DOI: 10.1137/19m127029x

Joel A. Rosenfeld, Benjamin P. Russo, Rushikesh Kamalapurkar, Taylor T. Johnson

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1643-1668, June 2024.
Abstract. This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new “kernel” function that represents an integration functional over a reproducing kernel Hilbert space (RKHS) dubbed an occupation kernel. The manuscript thoroughly explores the concept of occupation kernels in the contexts of RKHSs of continuous functions and establishes Liouville operators over RKHS, where several dense domains are found for specific examples of this unbounded operator. The combination of these two concepts allows for the embedding of a dynamical system into an RKHS, where function-theoretic tools may be leveraged for the examination of such systems. This framework allows for trajectories of a nonlinear dynamical system to be treated as a fundamental unit of data for a nonlinear system identification routine. The approach to nonlinear system identification is demonstrated to identify parameters of a dynamical system accurately while also exhibiting a certain robustness to noise.

SIAM 控制与优化期刊》第 62 卷第 3 期第 1643-1668 页，2024 年 6 月。摘要本手稿提出了一种新的非线性系统辨识方法，利用密集定义的Liouville算子和一种新的 "核 "函数（代表重现核希尔伯特空间（RKHS）上的积分函数，称为占位核）。手稿深入探讨了连续函数 RKHS 上下文中的占位核概念，并建立了 RKHS 上的刘维尔算子，为这种无界算子的特定示例找到了几个密集域。这两个概念的结合可以将动态系统嵌入到 RKHS 中，从而利用函数论工具来研究此类系统。通过这一框架，非线性动态系统的轨迹可被视为非线性系统识别程序的基本数据单元。这种非线性系统识别方法不仅能准确识别动态系统的参数，还能对噪声表现出一定的鲁棒性。

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引用次数: 0

Stability and Genericity of Bang-Bang Controls in Affine Problems 仿射问题中 Bang-Bang 控制的稳定性和通用性

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization

Pub Date : 2024-06-11 DOI: 10.1137/23m1586446

Alberto Domínguez Corella, Gerd Wachsmuth

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1669-1689, June 2024.
Abstract. We analyze the role of the bang-bang property in affine optimal control problems. We show that many essential stability properties of affine problems are only satisfied when minimizers are bang-bang. We employ Stegall’s variational principle to prove that almost any linear perturbation leads to a bang-bang strict global minimizer. Examples are given to show the applicability of our results to specific optimal control problems.

SIAM 控制与优化期刊》第 62 卷第 3 期第 1669-1689 页，2024 年 6 月。摘要我们分析了仿射最优控制问题中 bang-bang 特性的作用。我们证明，仿射问题的许多基本稳定性只有在最小化子为砰砰时才能满足。我们利用 Stegall 变分原理证明，几乎任何线性扰动都会导致砰砰严格全局最小化。我们举例说明了我们的结果在特定最优控制问题中的适用性。

引用次数: 0

Mean Viability Theorems and Second-Order Hamilton–Jacobi Equations 平均活力定理和二阶汉密尔顿-雅可比方程

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization

Pub Date : 2024-06-05 DOI: 10.1137/23m1550438

Christian Keller

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1615-1642, June 2024.
Abstract. We introduce the notion of mean viability for controlled stochastic differential equations and establish counterparts of Nagumo’s classical viability theorems (necessary and sufficient conditions for mean viability). As an application, we provide a purely probabilistic proof of a comparison principle and of existence for contingent and viscosity solutions of second-order fully nonlinear path-dependent Hamilton–Jacobi–Bellman equations. We do not use compactness and optimal stopping arguments, which are usually employed in the literature on viscosity solutions for second-order path-dependent PDEs.

SIAM 控制与优化期刊》第 62 卷第 3 期第 1615-1642 页，2024 年 6 月。摘要。我们引入了受控随机微分方程的平均可行度概念，并建立了南云经典可行度定理的对应定理（平均可行度的必要条件和充分条件）。作为应用，我们对二阶全非线性路径依赖哈密顿-雅各比-贝尔曼方程的或然解和粘性解的比较原理和存在性进行了纯概率证明。我们没有使用紧凑性和最优停止论证，这些论证通常在关于二阶路径依赖 PDE 的粘性解的文献中使用。

引用次数: 0

Randomized Optimal Stopping Problem in Continuous Time and Reinforcement Learning Algorithm 连续时间中的随机最优停止问题和强化学习算法

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization

Pub Date : 2024-06-03 DOI: 10.1137/22m1516725

Yuchao Dong

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1590-1614, June 2024.
Abstract. In this paper, we study the optimal stopping problem in the so-called exploratory framework, in which the agent takes actions randomly conditioning on the current state and a regularization term is added to the reward functional. Such a transformation reduces the optimal stopping problem to a standard optimal control problem. For the American put option model, we derive the related HJB equation and prove its solvability. Furthermore, we give a convergence rate of policy iteration and compare our solution to the classical American put option problem. Our results indicate a trade-off between the convergence rate and bias in the choice of the temperature constant. Based on the theoretical analysis, a reinforcement learning algorithm is designed and numerical results are demonstrated for several models.

SIAM 控制与优化期刊》第 62 卷第 3 期第 1590-1614 页，2024 年 6 月。摘要在本文中，我们研究了所谓探索框架下的最优停止问题，即代理根据当前状态随机采取行动，并在奖励函数中加入正则化项。这种转换将最优停止问题简化为一个标准的最优控制问题。对于美式看跌期权模型，我们推导出了相关的 HJB 方程，并证明了其可解性。此外，我们还给出了政策迭代的收敛率，并将我们的解决方案与经典美式看跌期权问题进行了比较。我们的结果表明，在选择温度常数时，收敛速度和偏差之间需要权衡。在理论分析的基础上，我们设计了一种强化学习算法，并对几个模型的数值结果进行了演示。

引用次数: 0

Invariance Principles for [math]-Brownian-Motion-Driven Stochastic Differential Equations and Their Applications to [math]-Stochastic Control 数学]-布朗运动驱动的随机微分方程的不变性原理及其在[数学]-随机控制中的应用

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization

Pub Date : 2024-05-29 DOI: 10.1137/23m1564936

Xiaoxiao Peng, Shijie Zhou, Wei Lin, Xuerong Mao

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1569-1589, June 2024.
Abstract. The G-Brownian-motion-driven stochastic differential equations (G-SDEs) as well as the G-expectation, which were seminally proposed by Peng and his colleagues, have been extensively applied to describing a particular kind of uncertainty arising in real-world systems modeling. Mathematically depicting long-time and limit behaviors of the solution produced by G-SDEs is beneficial to understanding the mechanisms of system’s evolution. Here, we develop a new G-semimartingale convergence theorem and further establish a new invariance principle for investigating the long-time behaviors emergent in G-SDEs. We also validate the uniqueness and the global existence of the solution of G-SDEs whose vector fields are only locally Lipschitzian with a linear upper bound. To demonstrate the broad applicability of our analytically established results, we investigate its application to achieving G-stochastic control in a few representative dynamical systems.

SIAM 控制与优化期刊》第 62 卷第 3 期第 1569-1589 页，2024 年 6 月。摘要。G-布朗运动驱动随机微分方程（G-SDEs）以及G-期望（G-expectation）是由彭晓赤和他的同事们从理论上提出的，已被广泛应用于描述现实世界系统建模中出现的一种特殊的不确定性。用数学方法描述 G-SDEs 所产生的解的长期和极限行为有利于理解系统的演化机制。在此，我们提出了一个新的 G-semartingale 收敛定理，并进一步建立了一个新的不变性原理，用于研究 G-SDE 中出现的长期行为。我们还以线性上界验证了矢量场仅为局部 Lipschitzian 的 G-SDE 解的唯一性和全局存在性。为了证明我们通过分析得出的结果的广泛适用性，我们研究了它在几个代表性动力学系统中实现 G-随机控制的应用。

引用次数: 0

Optimal Control of Stochastic Delay Differential Equations and Applications to Path-Dependent Financial and Economic Models 随机延迟微分方程的最优控制及其在路径依赖金融和经济模型中的应用

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization

Pub Date : 2024-05-20 DOI: 10.1137/23m1553960

Filippo De Feo, Salvatore Federico, Andrzej Święch

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1490-1520, June 2024.
Abstract. In this manuscript we consider a class of optimal control problems of stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we characterize the value function of the problem as the unique viscosity solution of the associated infinite-dimensional Hamilton-Jacobi-Bellman equation. Finally, we prove a [math]-partial regularity of the value function. We apply these results to path dependent financial and economic problems (Merton-like portfolio problem and optimal advertising).

SIAM 控制与优化期刊》第 62 卷第 3 期第 1490-1520 页，2024 年 6 月。摘要在本手稿中，我们考虑了一类随机微分延迟方程的最优控制问题。首先，我们在合适的无穷维希尔伯特空间中重写问题。然后，利用动态编程方法，我们将问题的值函数表征为相关无穷维汉密尔顿-雅各比-贝尔曼方程的唯一粘性解。最后，我们证明了值函数的[数学]部分正则性。我们将这些结果应用于路径依赖的金融和经济问题（类似默顿的投资组合问题和最优广告）。

引用次数: 0

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数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

SIAM Journal on Control and Optimization

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

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