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扩展截尾的随机逼近算法

陈翰馥   

  1. 中国科学院数学与系统科学院系统控制重点实验室, 北京 100190
  • 收稿日期:2012-01-07 出版日期:2012-12-25 发布日期:2013-03-13

陈翰馥. 扩展截尾的随机逼近算法[J]. 系统科学与数学, 2012, 32(12): 1472-1487.

CHEN Han-Fu. STOCHASTIC APPROXIMATION ALGORITHMS WITH EXPANDING TRUNCATIONS[J]. Journal of Systems Science and Mathematical Sciences, 2012, 32(12): 1472-1487.

STOCHASTIC APPROXIMATION ALGORITHMS WITH EXPANDING TRUNCATIONS

CHEN Han-Fu   

  1. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Beijing 100190
  • Received:2012-01-07 Online:2012-12-25 Published:2013-03-13
注意到系统控制及相关领域中相当一类问题可归结为参数估计,而后者又可转化为未知函数的求根问题, 首先介绍用带噪声量测递推地求根方法, 即经典的随机逼近算法, 并针对它的不足,引入扩展截尾的随机逼近算法(SAAWET),给出它的一般收敛定理.接着介绍应用SAAWET解决线性随机系统系数辨识及定阶, Hammerstein, Wiener, NARX等非线性系统的辨识,非线性随机系统的迭代学习控制及适应调节, 以及其它一些问题.所给出的估计都是递推的, 并且以概率1 收敛到真值.
It is noticed that a considerable class of problems arising from systems and control and related fields may be reduced to parameter estimation, which, in turn, can be transformed to a root-seeking problem for unknown functions. The paper first introduces the root-seeking method based on the noisy observations, i.e., the classical stochastic approxi- mation algorithm. Against the restrictions of applying the classical algorithm, the stochastic approximation algorithm with expanding truncations (SAAWET) is introduced, and its general convergence theorem is demonstrated as well. Then, SAAWET is applied to solve problems like coefficient identification and order determination of linear stochastic systems, identification of Hammerstein, Wiener, and NARX systems, iterative learning control and adaptive regula- tion for nonlinear stochastic systems, and some others. All estimates given by the method are recursive and converge to the corresponding true values with probability one.

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