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# 数学代写|最优化作业代写optimization theory代考|CONCLUDING REMARKS

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## 数学代写|最优化作业代写optimization theory代考|CONCLUDING REMARKS

In control system design, the ultimate objective is to obtain a controller that will cause a system to perform in a desirable manner. Usually, other factors, such as weight, volume, cost, and reliability also influence the controller design, and compromises between performance requirements and implementation considerations must be made. Classical design procedures are best suited for linear, single-input, single-output systems with zero initial conditions. Using simulation, mathematical analysis, or graphical methods, the designer evaluates the effects of inserting various physical devices into the system. By trial and error either an acceptable controller design is obtained, or the designer concludes that the performance requirements cannot be satisfied.

Many complex aerospace problems that are not amenable to classical techniques have been solved by using optimal control theory. However, we are forced to admit that optimal control theory does not, at the present time, constitute a generally applicable procedure for the design of simple controllers. The optimal control law, if it can be obtained, usually requires a digital computer for implementation (an important exception is the linear regulator problem discussed in Section 5.2), and all of the states must be available for feedback to the controller. These limitations may preclude implementation of the optimal control law; however, the theory of optimal control is still useful, because

1. Knowing the optimal control law may provide insight helpful in designing a suboptimal, but easily implemented controller.
2. The optimal control law provides a standard for evaluating proposed suboptimal designs. In other words, by knowing the optimal control law we have a quantitative measure of performance degradation caused by using a suboptimal controller.

## 数学代写|最优化作业代写optimization theory代考|PERFORMANCE MEASURES FOR OPTIMAL CONTROL PROBLEMS

The “optimal control problem” is to find a control $\mathbf{u}^* \in U$ which causes the system
$$\dot{\mathbf{x}}(t)=\mathbf{a}(\mathbf{x}(t), \mathbf{u}(t), t)$$

to follow a trajectory $\mathbf{x}^* \in X$ that minimizes the performance measure
$$J=h\left(\mathbf{x}\left(t_f\right), t_f\right)+\int_{t_0}^{t_s} g(\mathbf{x}(t), \mathbf{u}(t), t) d t .$$
Let us now discuss some typical control problems to provide some physical motivation for the selection of a performance measure.
Minimum-Time Problems
Problem: To transfer a system from an arbitrary initial state $\mathbf{x}\left(t_0\right)=\mathbf{x}0$ to a specified target set $S$ in minimum time. The performance measure to be minimized is \begin{aligned} J & =t_f-t_0 \ & =\int{t_0}^{t s} d t, \end{aligned}
with $t_f$ the first instant of time when $\mathbf{x}(t)$ and $S$ intersect. The automobile example discussed in Section 1.1 is a minimum-time problem. Other typical examples are the interception of attacking aircraft and missiles, and the slewing mode operation of a radar, or gun system.

## 数学代写|最优化作业代写optimization theory代考|PERFORMANCE MEASURES FOR OPTIMAL CONTROL PROBLEMS

“最优控制问题”是找到一个控制$\mathbf{u}^* \in U$，使系统
$$\dot{\mathbf{x}}(t)=\mathbf{a}(\mathbf{x}(t), \mathbf{u}(t), t)$$

$$J=h\left(\mathbf{x}\left(t_f\right), t_f\right)+\int_{t_0}^{t_s} g(\mathbf{x}(t), \mathbf{u}(t), t) d t .$$

## 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。