解系统控制问题的递推方法

Recursive approach to solving problems from systems and control

中文关键词  系统控制  递推解法  随机逼近  系统辨识  适应调节

英文关键词  system and control  recursive solution  stochastic approximation  system identification  adaptive regulation

中文摘要

      本文对系统控制及其他领域中的一大类问题, 介绍一种递推解法, 使当数据增加时, 递推解以概率1收敛到真解. 这方法主要以3个步骤来实现: 首先, 把欲解的问题参数化; 然后, 选择适用的递推参数估计算法; 最后, 证明递推估计收敛到笔者想要的值. 文中列举了具体的系统控制问题, 展示如何把它们参数化. 作为递推估计算法, 文中介绍了扩展截尾的随机逼近算法(SAAWET), 给出了它的一般收敛定理. 随后, 以两个系统控制问题, 展示该方法的具体实现, 所附模拟计算实例证实了该方法. 实际上, 这种方法已成功地解决了系统控制及其他相关领域中的一系列问题.

英文摘要

      A recursive approach to solving a large class of problems arising from systems and control and other areas is introduced. The essence of the method consists of three steps: First, the problem under consideration is parameterized; Second, an appropriate recursive parameter estimation method is selected; Finally, the recursive estimate is proved to converge to the sought-for value. In the paper, parametrization of two problems from systems and control is demonstrated. To serve as the recursive estimation method, the stochastic approximation algorithm with expanding truncations (SAAWET) is introduced, and its general convergence theorem is presented. Then, the two parameterized problems from system and control are actually solved by the proposed approach. The attached numerical examples have justified the method. As a matter of fact, a series of problems from systems and control and other related areas have successfully been solved by the approach.