最优控制及应用
最优控制及应用
摘要:最优控制是最优化方法的一个应用。最优控制,又称动态最优化,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。
最优化一般可以分为最优设计、最优计划、最优管理和最优控制四个方面。而最优控制理论是研究和解决从一切可能的控制方案中寻找最优解的一门学科,解决最优控制问题的主要方法有古典变分法、极大值原理和动态规划。最优控制理论已被应用于综合和设计最速控制系统、最省燃料控制系统、最小能耗控制系统、线性调节器等。同时本文也介绍了最优控制理论的新进展,即在线优化方法(局部参数最优化和整体最优化设计方法、预测控制中的滚动优化算法、稳态阶梯控制、系统优化和参数估计的集成研究方法)和智能优化方法(神经网络优化方法、遗传算法、模糊优化方法)。
关键词:最优化;最优控制;遗传算法
Optimum Control and Applications
Abstract: The optimum control is an application of optimization methods and is also called dynamic optimization, being the most fundamental and the most central part of the modern control theory. Its studied central problem is how to decide the control law on the basis of dynamic characteristics of the controlled system so that the system operates according to technical requirements and a certain indicator, which describes the system performance or quality, is optimized in a certain sense. The four key points of optimum control are the dynamic systems as the controlled plant, initial condition and terminal condition (time and state) and performance index and admissible control.
The optimization consists of optimal design, optimal plan, optimal management and optimal control. The optimal control theory is a subject of studying and finding the optimal solution from all possible control plans. The main solutions of solving optimal control problems include the classical variation methods, maximum principles as well as dynamic planning. The optimal control theory has been applied to comprehensive and designed time optimal control systems, minimum fuel control systems, minimum energy-control systems, linear regulators and so on. Besides, the paper also introduces the new development of optimal control theory, that is, on-line optimization methods, (which includes optimal design methods of local parameters and the overall parameters, rolling optimizing methods of predictive control, steady stair-like control and integration methods of system optimization and parameter estimation) and intelligent optimization methods, which covers neural network optimization methods, genetic algorithm and fuzzy optimal methods.
Key Words: Optimization, Optimum control, Genetic algorithm