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• 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

## 金融代写|金融工程作业代写Financial Engineering代考|Main Approaches to Nonlinear Control

In control and stabilization of the dynamics of financial systems, one can distinguish three main research axes: (i) Methods of global linearization, (ii) Methods of asymptotic linearization, and (iii) Lyapunov methods, As far as approach (i) is concerned, that is methods of global linearization, these aim at the transformation of the nonlinear dynamics of the system to equivalent linear state-space descriptions for which one can design controllers using state feedback and can also solve the associated state estimation (filtering) problem. One can classify here methods based on the theory of differentially flat systems and methods based on Lie algebra. As far as approach (ii) is concerned, solutions are pursued to the problem of nonlinear control with the use of local linear models (obtained at local equilibria). For such local linear models, feedback controllers of proven stability can be developed. One can select the parameters of such local controllers in a manner that assures the robustness of the control loop to both external perturbations and to model parametric uncertainty. As far as approach (iii) is concerned, that is methods of nonlinear control of the Lyapunov type one comes against problems of minimization of Lyapunov functions so as to assure the asymptotic stability of the control loop. For the development of Lyapunov type controllers one can either exploit a model about the systems dynamics or can proceed in a model-free manner, as in the case of indirect adaptive control.

## 金融代写|金融工程作业代写Financial Engineering代考|Overview of Main Approaches to Nonlinear Control

One can note three axes in the development of nonlinear control systems based on state-space representation of the system’s dynamics: (1) Methods of global linearization-based control (2) Methods of asymptotic linearization-based control, and (3) Lyapunov theory-based methods of control $[121,216,222,225,228,248] .$

As far as approach (i) is concerned, that is methods of global linearization these aim at the transformation of the nonlinear dynamics of the system to equivalent linear state-space descriptions for which one can design controllers using state feedback and can also solve the associated state estimation (filtering) problem. One can classify here methods based on the theory of differentially flat systems and methods based on Lie algebra. These approaches avoid approximate modelling errors and arrive at controllers of elevated precision and robustness. Using global linearization methods one can also solve nonlinear state estimation (filtering) problems.

As far as approach (ii) is concerned that is methods of asymptotic linearization, one can note results on robust and adaptive control with the use of a decomposition of the systems dynamics into local linear models. Solution to the problem of nonlinear control with the use of local linear models (obtained at local equilibria) is often pursued. For such local linear models, feedback controllers of proven stability can be developed. One can select the parameters of such local controllers in a manner that assures the robustness of the control loop to both external perturbations and to model parametric uncertainty. These controllers succeed asymptotically (that is as time advances) the compensation of the systems nonlinear dynamics and the stabilization of the closed control loops. In this area, one can apply robust control which is based on local approximate linearization of the systems dynamics and which requires the computation of Jacobian matrices, Such a method can solve the nonlinear $\mathrm{H}$-infinity control problem.

As far as approach (iii) is concerned, that is methods of nonlinear control of the Lyapunov type the minimization of Lyapunov functions is pursued so as to assure the asymptotic stability of the control loop. For the development of Lyapunov type controllers one can either exploit a model about the systems dynamics or can proceed in a model-free manner, as in the case of indirect adaptive control. In the latter approach, the systems dynamics is taken to be completely unknown and can be approximated by adaptive algorithms which are suitably designed so as to assure the stabilization and robustness of the control loop.

# 金融工程代写

## 有限元方法代写

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## 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。

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