文档介绍：湖北民族学院
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摘要
最优控制,又称无穷维最优化或动态最优化,是现代控制理论的最基本,最核心的部分。它所研究的中心问题是:如何根据受控系统的动态特性,去选择控制规律,才能使得系统按照一定的技术要求进行运转,并使得描述系统性能或品质的某个“指标”在一定的意义下达到最优值。最优控制问题有四个关键点:受控对象为动态系统;初始与终端条件(时间和状态);性能指标以及容许控制。
一个典型的最优控制问题描述如下:被控系统的状态方程和初始条件给定,同时给定目标函数。然后寻找一个可行的控制方法使系统从输出状态过渡到目标状态,并达到最优的性能指标。系统最优性能指标和品质在特定条件下的最优值是以泛函极值的形式来表示。因此求解最优控制问题归结为求具有约束条件的泛函极值问题,属于变分学范畴。变分法、最大值原理(最小值原理)和动态规划是最优控制理论的基本内容和常用方法。庞特里亚金极大值原理、贝尔曼动态规划以及卡尔曼线性二次型最优控制是在约束条件下获得最优解的三个强有力的工具,应用于大部分最优控制问题。尤其是线性二次型最优控制,因为其在数学上和工程上实现简单,故其有很大的工程实用价值。
关键词:最优控制; 控制规律; 最优性能指标; 线性二次型
Abstract
The optimal control, also called dynamic optimization or infinite dimension, optimization of modern control theory, the most basic part of the core. It is the center of the research question: how to control system based on the dynamic characteristics, to choose, can control system according to certain technical requirements, and makes the operation performance of the system or the quality of describing a "index" in certain significance to achieve optimal value. The optimal control problem has four points for dynamic systems, controlled, The initial and terminal conditions (state) and, Performance index and allow control.
A typical of optimal control problem is described as follows: the state equation and initial conditions are given, and given the objective function. Then a feasible method for the control system of the output state transition to the target state and optimum performance. The optimal performance index and quality in the specific conditions of the optimal value is functional form. Therefore solution of optimal control problem is due to the constraint condition of functional, belongs to the category of variational learning. The variational method, the maximum principle (minimum principle) and dynamic planning is the optimal control theory, the basic contents and methods. The Pontryagin maximum principle, Behrman dynamic programming and Kaman linear quadratic optimal control is obtained in the constraint condition of