• 论文 •

### 扩展截尾的随机逼近算法

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

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

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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