### 统计代写|随机控制代写Stochastic Control代考|Challenges of Structural Control in Civil Engineering

statistics-lab™ 为您的留学生涯保驾护航 在代写随机控制Stochastic Control方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写随机控制Stochastic Control代写方面经验极为丰富，各种代写随机控制Stochastic Control相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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.

(i) 与动态激励相关的挑战

(ii) 与结构参数有关的挑战

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。