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• 出版日期:2021-02-25 发布日期:2021-02-02

. [J]. 系统科学与复杂性, 2021, 34(1): 236-250.

ZHANG Yaqi · GUO Lei. Convergence of Self-Tuning Regulators Under Conditional Heteroscedastic Noises with Unknown High-Frequency Gain[J]. Journal of Systems Science and Complexity, 2021, 34(1): 236-250.

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

ZHANG Yaqi · GUO Lei

1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
Email: zhangyq@amss.ac.cn; lguo@amss.ac.cn.
• Online:2021-02-25 Published:2021-02-02

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.

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