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随机控制或随机最优控制是控制理论的一个子领域，它涉及到观察中或驱动系统演变的噪声中存在的不确定性。
随机控制或随机最优控制是控制理论的一个子领域，它涉及到观察中或驱动系统进化的噪声中存在的不确定性。系统设计者以贝叶斯概率驱动的方式假设，具有已知概率分布的随机噪声会影响状态变量的演变和观察。随机控制的目的是设计受控变量的时间路径，以最小的成本执行所需的控制任务，尽管存在这种噪声，但以某种方式定义。
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我们提供的随机控制Stochastic Control及其相关学科的代写，服务范围广, 其中包括但不限于:
- Statistical Inference 统计推断
- Statistical Computing 统计计算
- Advanced Probability Theory 高等概率论
- Advanced Mathematical Statistics 高等数理统计学
- (Generalized) Linear Models 广义线性模型
- Statistical Machine Learning 统计机器学习
- Longitudinal Data Analysis 纵向数据分析
- Foundations of Data Science 数据科学基础
统计代写|随机控制代写Stochastic Control代考|Challenges of Structural Control in Civil Engineering
The control theory and methods were thrived in the fields of electronics and information engineering, mechanical engineering, aerospace engineering, etc. They focus on the state regulation of systems under distributions such as random excitations and measurement noise, while new challenging issues have to be encountered when these achievements are applied into the field of civil engineering. Different from the practical demands, however, as emerged in the mechanical engineering and aerospace
engineering, there are more uncertainty and higher complexity inherent in civil engineering. The structural control in civil engineering involves a variety of practical challenges such as the structural safety, system durability, structural comfortability, etc. Moreover, large output and high performance are claimed as to the control devices. The challenging issues of structural control in civil engineering that are distinguished from the classical control theory and methods lie in dynamic excitations, structural parameters, nonlinear effects, control law formulas, and control modalities.
(i) Challenges related to dynamic excitations
In the period of service, the civil engineering structures usually suffer from the dynamic excitations, especially from the risk of hazardous dynamic actions. The hazardous dynamic actions such as strong earthquakes, high winds, and huge waves exhibit significant randomness inherent in their occurring time, occurring space, and occurring intensity. The influences of random excitations upon the accurate quantification of structural state and the logical design of control systems are thus prominent. The classical stochastic optimal control theory, derived from the Itô stochastic differential equation, is restricted to the assumption of white Gaussian noise excitations and measurement noise. It still lacks the sufficient exploration into the case under the general random excitations. This limitation owes to the fact the classical stochastic optimal control theory has been mostly applied in the nonmechanical problems such as those raised from the mechanical engineering and aerospace engineering. While the challenges related to the random excitation become predominant, the stochastic optimal control theory is used to deal with the mechanical problems that occur in the civil engineering. In fact, the seismic ground motion exhibits significant nonstationarities, and the high wind even just the stable airflow exhibits certain nonstationarities. However, the random excitations in the classical stochastic optimal control are almost assumed to be stationary white Gaussian noise, which is obviously far from the hazardous dynamic actions upon the civil engineering structures.
(ii) Challenges related to structural parameters
Due to the uncertainties inherent in the structural materials and manufactures, the basic parameters of civil engineering structures usually exhibit randomness. This brings about a series of new issues to the structural control. The influences of random parameters upon the stochastic optimal control of structures give rise to two aspects. One is the state estimation. The Kalman filter theory is a celebrated method for dealing with the measurement noise and the incomplete measurement in the classical system control. How this method is applied to state estimation of structures with random parameters constitutes a new challenge. The other is the stability of control system. The presence of random parameters leads to the issue of stochastic eigenvalues, which also brings about a new challenge to the Lyapunov stability theory based stability analysis of classical control systems.
统计代写|随机控制代写Stochastic Control代考|Physically Based Stochastic Optimal Control
It is readily recognized that the relevant theory and methods of classical stochastic optimal control are all developed on the basis of Itô calculus, which underlies the state equation of systems. This treatment allows an exclusive assumption that the external excitation is viewed as a white Gaussian noise or a filtered white Gaussian noise, which is far from the real engineering excitations. This assumption thus limits the engineering application of the classical stochastic optimal control in practice. In fact, the assumption hinders the development of the modern theory of stochastic dynamical system as well. Just in view of this situation, the probability density evolution method was developed based on the probability preservation principle. The PDEM bridges the essential relation between the probability density evolution and the physical state evolution of systems, that is, the physical state evolution of systems drives the probbabbility density evoolution. Thẽ dêtêministic systêm and the stōchāstic system can thus be summarized into a unified framework ( $\mathrm{Li}$ and Chen 2009). Moreover, this progress profoundly reveals that the physical evolution mechanism of systems is still the critical content of stochastic system researches, which underlies the theory of physical stochastic system. In this framework, a novel theory and the associated methods for the stochastic optimal control of structures are expected to develop.
In the end nineteenth century, the research of practical systems with random initial state formed the basis of the Gibbs-Liouville theory, and proved the celebrated Liouville equation (Syski 1967). It is Einstein who addressed the special cases of diffusion processes and established the diffusion equation for Brownian motion in 1905 (Einstein 1905). Then it was extended by Fokker and Planck who derived the classical Fokker-Planck equation (Fokker 1914; Planck 1917). In 1931, Kolmogorov independently deduced a same formulation as the Fokker-Planck equation, and a backward Kolmogorov equation was then derived (Kolmogorov 1931). Owing to the rigorous mathematical basis, the Kolmogorov equation is so-called the FokkerPlanck-Kolmogorov equation (FPK equation). Thereafter, the FPK equation and its solutions formed the primary topics of random vibration theory. In 1957, Dostupov and Pugachev attempted to quantify the randomness inherent in the system input through introducing the Karhunen-Loeve decomposition (Dostupov and Pugachev 1957). It is the so-called Dostupov-Pugachev equation. It is regret; however, the equations mentioned above are all high-dimensional and strong-coupling partial differential equations, of which the analytical solutions are hardly derived. Li and Chen explored the probability preservation principle in an elegant manner, and secured the essential relation between probability density evolution and physical state evolution of systems. A family of decoupling probability density evolution equations, i.e., the so-called generalized probability density evolution equation (GDEE), was then proposed in the past 15 years (Li and Chen $2006 \mathrm{a}, \mathrm{b}, \mathrm{c}, 2008,2009$ ). It is recognized that the GDEE accommodates the randomness both inherent in external excitations and in structural systems, which provides a new way to carry out the response analysis and reliability assessment of stochastic systems subjected to general random excitations, and also allows a potential for stochastic optimal control of linear and nonlinear multi-degree-of-freedom systems.
统计代写|随机控制代写Stochastic Control代考|Scope of the Book
In the civil engineering community, the objective of structural control is often definite, while the loads acting on the engineering structures cannot be predicted accurately, especially for the dynamic excitations. Therefore, the stochastic optimal control of structures considering the randomness inherent in engineering excitations ought to be paid sufficient attention. For this reason, the present book focuses on the hazardous dynamic actions, specifically on the random seismic ground motion and the
fluctuating wind-velocity field, and devotes to developing a novel theory and the pertinent successful strategies for stochastic optimal control of engineering structures, in conjunction with the probability density evolution method. The outline is sketched as follows: the performance evolution of controlled systems is first investigated, and a family of probabilistic criteria in terms of structural responses is then established; the generalized optimal control policy and the associated control law involving the simultaneous optimization of the controller parameters and the control device placement are then proposed; in order to verify the propused methodulogy, a scries of engineering applications and experimental studies of controlled structures are then introduced.
The scope of the book is illustrated as follows:
In Chap. 2, the associated theoretical principles pertaining to the physically based stochastic optimal control are addressed, including the classical stochastic optimal control in the framework of the stochastic maximum principle and the stochastic dynamic programming, the random vibration of linear and nonlinear structures, the dynamic reliability of structures, and the modeling of random dynamic excitations. The kernel equation of the PDEM, i.e., the generalized probability density evolution equation, is introduced as well. This chapter devotes to providing a solid foundation for the successive developments of theory and methods of stochastic optimal control of structures.
In Chap. 3, the probability density evolution method of stochastic optimal control is detailed. Performance evolution of controlled structural systems is first investigated. The solution of the physically based stochastic optimal control is deduced according to Pontryagin’s maximum principle. Active stochastic optimal control based on the probabilistic criterion on system second-order statistics evaluation is discussed. For validating purposes, comparative studies against the classical LQG control are carried out.
In Chap. 4 , a family of probabilistic criteria for the physically based stochastic optimal control is proposed, including the single-objective optimization criteria with respect to the second-order moments such as the mean and the variance, and with respect to the tail of probability density, i.e., the exceedance probability, of equivalent extreme-value responses: and the multiple-objective optimization criteria with respect to the mean and the exceedance probability of equivalent extreme-value responses in performance trade-off and in energy trade-off, respectively. Numerical examples are studied to prove the applicability of the proposed probabilistic criteria.
In Chap. 5, the concept of generalized optimal control policy is proposed. This concept indicates a unified formula of the optimal control law with optimized controller parameters pertaining to passive, active, semiactive, and hybrid controls, and with optimized control device placement. In order to attain the optimal placement of control devices at each sequential step, a probabilistic controllability index in argument of exceedance probability is defined. Comparative studies between control device deployment strategies using the minimum controllability index gradient criterion and the maximum controllability index criterion are then carried out.
随机控制代写
统计代写|随机控制代写Stochastic Control代考|Challenges of Structural Control in Civil Engineering
控制理论和方法在电子与信息工程、机械工程、航空航天工程等领域蓬勃发展，重点关注随机激励和测量噪声等分布下系统的状态调控，同时也面临着新的挑战性问题当这些成果应用到土木工程领域时。然而，与机械工程和航空航天领域出现的实际需求不同
工程，土木工程固有更多的不确定性和更高的复杂性。土木工程中的结构控制涉及结构安全性、系统耐久性、结构舒适性等多种实际挑战。此外，控制装置还要求大输出和高性能。土木工程中结构控制与经典控制理论和方法不同的挑战性问题在于动态激励、结构参数、非线性效应、控制律公式和控制模态。
(i) 与动态激励相关的挑战
在使用期间，土木工程结构通常会受到动力激励，尤其是危险动力作用的风险。强地震、大风、巨浪等危险动力作用在其发生时间、发生空间和发生强度方面表现出明显的随机性。因此，随机激励对结构状态准确量化和控制系统逻辑设计的影响非常突出。源自伊藤随机微分方程的经典随机最优控制理论仅限于假设高斯白噪声激励和测量噪声。对一般随机激励下的情况还缺乏足够的探索。这种限制是由于经典随机最优控制理论主要应用于非机械问题，例如从机械工程和航空航天工程中提出的问题。虽然与随机激励相关的挑战成为主要挑战，但随机最优控制理论用于处理土木工程中出现的机械问题。事实上，地震地震动表现出显着的非平稳性，大风即使只是稳定的气流也表现出一定的非平稳性。然而，经典随机最优控制中的随机激励几乎被假定为平稳的高斯白噪声，这显然与对土木工程结构的危险动力作用相去甚远。
(ii) 与结构参数有关的挑战
由于结构材料和制造固有的不确定性，土木工程结构的基本参数通常表现出随机性。这给结构控制带来了一系列新问题。随机参数对结构随机最优控制的影响体现在两个方面。一是状态估计。卡尔曼滤波理论是处理经典系统控制中测量噪声和不完全测量的著名方法。如何将这种方法应用于具有随机参数的结构的状态估计是一个新的挑战。二是控制系统的稳定性。随机参数的存在导致随机特征值的问题，
统计代写|随机控制代写Stochastic Control代考|Physically Based Stochastic Optimal Control
很容易认识到，经典随机最优控制的相关理论和方法都是在伊藤演算的基础上发展起来的，伊藤演算是系统状态方程的基础。这种处理允许一个唯一的假设，即外部激励被视为高斯白噪声或过滤的高斯白噪声，这与真实的工程激励相去甚远。因此，这一假设限制了经典随机最优控制在实践中的工程应用。事实上，这一假设也阻碍了现代随机动力系统理论的发展。正是针对这种情况，基于概率守恒原理发展了概率密度演化方法。PDEM桥接了概率密度演化与系统物理状态演化之间的本质关系，即系统物理状态演化驱动概率密度演化。Thẽ dêtêministic 系统和随机系统因此可以概括为一个统一的框架（大号一世和陈 2009）。此外，这一进展深刻地揭示了系统的物理演化机制仍然是随机系统研究的关键内容，是物理随机系统理论的基础。在此框架下，有望发展一种结构随机最优控制的新理论和相关方法。
十九世纪末，对具有随机初始状态的实际系统的研究形成了吉布斯-刘维尔理论的基础，并证明了著名的刘维尔方程（Syski 1967）。爱因斯坦在 1905 年解决了扩散过程的特殊情况并建立了布朗运动的扩散方程（Einstein 1905）。然后它被 Fokker 和 Planck 扩展，他们推导出了经典的 Fokker-Planck 方程（Fokker 1914；Planck 1917）。1931 年，Kolmogorov 独立推导出了与 Fokker-Planck 方程相同的公式，然后推导出了一个反向 Kolmogorov 方程（Kolmogorov 1931）。由于严格的数学基础，Kolmogorov方程被称为FokkerPlanck-Kolmogorov方程（FPK方程）。此后，FPK 方程及其解构成了随机振动理论的主要课题。1957 年，Dostupov 和 Pugachev 试图通过引入 Karhunen-Loeve 分解来量化系统输入中固有的随机性（Dostupov 和 Pugachev 1957）。这就是所谓的 Dostupov-Pugachev 方程。是遗憾；但上述方程都是高维强耦合偏微分方程，很难得到解析解。Li 和 Chen 优雅地探索了概率守恒原理，确定了概率密度演化与系统物理状态演化的本质关系。解耦概率密度演化方程族，即所谓的广义概率密度演化方程（GDEE），2006一种,b,C,2008,2009）。人们认识到，GDEE 适应了外部激励和结构系统中固有的随机性，这为对受到一般随机激励的随机系统进行响应分析和可靠性评估提供了一种新方法，也为随机优化提供了可能。控制线性和非线性多自由度系统。
统计代写|随机控制代写Stochastic Control代考|Scope of the Book
在土木工程界，结构控制的目标往往是明确的，而作用在工程结构上的载荷无法准确预测，尤其是动态激励。因此，考虑工程激励固有随机性的结构随机最优控制应引起足够的重视。出于这个原因，本书侧重于危险的动力作用，特别是随机地震地面运动和
波动风速场，并致力于结合概率密度演化方法开发工程结构随机最优控制的新理论和相关成功策略。概述如下：首先研究受控系统的性能演变，然后建立一系列关于结构响应的概率标准；然后提出了涉及控制器参数同时优化和控制装置布置的广义最优控制策略和相关控制律；为了验证所提出的方法，然后介绍了一系列工程应用和受控结构的实验研究。
本书的范围如下图所示：
在第一章。2、阐述了与基于物理的随机最优控制相关的理论原理，包括在随机最大值原理和随机动态规划框架下的经典随机最优控制、线性和非线性结构的随机振动、动态可靠性结构，以及随机动态激励的建模。还介绍了PDEM的核方程，即广义概率密度演化方程。本章旨在为结构随机最优控制理论和方法的不断发展奠定坚实的基础。
在第一章。3、详细介绍了随机最优控制的概率密度演化方法。首先研究受控结构系统的性能演变。根据Pontryagin极大原理推导出基于物理的随机最优控制的解。讨论了基于概率准则的系统二阶统计评价主动随机最优控制。出于验证目的，对经典 LQG 控制进行了比较研究。
在第一章。如图4所示，提出了一系列基于物理的随机最优控制的概率准则，包括关于均值和方差等二阶矩的单目标优化准则，以及关于概率密度尾部的单目标优化准则，即，等效极值响应的超过概率： 以及在性能权衡和能量权衡中分别关于等效极值响应的均值和超出概率的多目标优化标准。研究了数值例子来证明所提出的概率标准的适用性。
在第一章。5、提出广义最优控制策略的概念。这个概念表明了最优控制律的统一公式，其中包含与被动、主动、半主动和混合控制相关的优化控制器参数，以及优化的控制装置布置。为了在每个连续步骤中实现控制装置的最佳布置，定义了以超过概率为参数的概率可控性指标。然后对使用最小可控性指标梯度准则和最大可控性指标准则的控制装置部署策略进行了比较研究。
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金融工程代写
金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。
非参数统计代写
非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。
广义线性模型代考
广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。
术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。
有限元方法代写
有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。
有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。
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随机分析代写
随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。
时间序列分析代写
随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。
回归分析代写
多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。
MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习和应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。