Convergence of Self-Tuning Regulators Under Conditional Heteroscedastic Noises with Unknown High-Frequency Gain  

作　　者：ZHANG Yaqi GUO Lei 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Journal of Systems Science & Complexity》2021年第1期236-250,共15页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.11688101。

摘　　要：In the classical theory of self-tuning regulators, it always requires that the conditional variances of the systems noises are bounded. However, such a requirement may not be satisfied when modeling many practical systems, and one significant example is the well-known ARCH(autoregressive conditional heteroscedasticity) model in econometrics. The aim of this paper is to consider self-tuning regulators of linear stochastic systems with both unknown parameters and conditional heteroscedastic noises, where the adaptive controller will be designed based on both the weighted least-squares algorithm and the certainty equivalence principle. The authors will show that under some natural conditions on the system structure and the noises with unbounded conditional variances, the closed-loop adaptive control system will be globally stable and the tracking error will be asymptotically optimal.Thus, this paper provides a significant extension of the classical theory on self-tuning regulators with expanded applicability.

关 键 词：ARCH model conditional heteroscedasticity CONVERGENCE self-tuning regulator weighted least-squares algorithm 

分 类 号：O231[理学—运筹学与控制论]