Convergence of Self-Tuning Regulators under Conditional Heteroscedastic Noises with Unknown High-Frequency Gain |
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Authors: | Zhang Yaqi Guo Lei |
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Institution: | 1.Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China ; |
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Abstract: | 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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