Convergence of Self-Tuning Regulators under Conditional Heteroscedastic Noises
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- 英文论文题名：Convergence of Self-Tuning Regulators under Conditional Heteroscedastic Noises
- 论文作者：Yaqi Zhang ; Lei Guo
- 英文论文作者：Yaqi Zhang ; Lei Guo ; Key Laboratory of Systems and Control ; AMSS ; Chinese Academy of Sciences
- 年：2017
- 作者机构：Key Laboratory of Systems and Control,AMSS,Chinese Academy of Sciences;
- 英文论文关键词：Self-Tuning Regulator ; Conditional Heteroscedasticity ; ARCH Model ; Weighted Least-Squares Algorithm ; Convergence
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：TP214;TP273
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：200k
- 原文格式：D
- 会议级别：全国
摘要
Traditional convergence theory of self-tuning regulators requires boundedness of the conditional variances of the systems noise processes. However, this requirement cannot be satisfied for many practical models such the well-known ARCH(Autoregressive Conditional Heteroscedasticity) model in economic systems. The aim of this paper is to provide a convergence theory of self-tuning regulators for linear uncertain systems with conditional heteroscedastic noises, where the conditional variance is unbounded. To be specific, we consider weighted least-squares-based self-tuning regulators, and establish both the global stability and the optimality of tracking under some natural conditions on the system models as well as on the conditional heteroscedastic noises. To the best of the authors' knowledge, this is the first paper that investigates this kind of problems with a convergence theory, and makes the self-tuning regulators applicable to systems with noised modeled by ARCH.
Traditional convergence theory of self-tuning regulators requires boundedness of the conditional variances of the systems noise processes. However, this requirement cannot be satisfied for many practical models such the well-known ARCH(Autoregressive Conditional Heteroscedasticity) model in economic systems. The aim of this paper is to provide a convergence theory of self-tuning regulators for linear uncertain systems with conditional heteroscedastic noises, where the conditional variance is unbounded. To be specific, we consider weighted least-squares-based self-tuning regulators, and establish both the global stability and the optimality of tracking under some natural conditions on the system models as well as on the conditional heteroscedastic noises. To the best of the authors' knowledge, this is the first paper that investigates this kind of problems with a convergence theory, and makes the self-tuning regulators applicable to systems with noised modeled by ARCH.
Traditional convergence theory of self-tuning regulators requires boundedness of the conditional variances of the systems noise processes. However, this requirement cannot be satisfied for many practical models such the well-known ARCH(Autoregressive Conditional Heteroscedasticity) model in economic systems. The aim of this paper is to provide a convergence theory of self-tuning regulators for linear uncertain systems with conditional heteroscedastic noises, where the conditional variance is unbounded. To be specific, we consider weighted least-squares-based self-tuning regulators, and establish both the global stability and the optimality of tracking under some natural conditions on the system models as well as on the conditional heteroscedastic noises. To the best of the authors' knowledge, this is the first paper that investigates this kind of problems with a convergence theory, and makes the self-tuning regulators applicable to systems with noised modeled by ARCH.
引文
[1]L.Guo.A retrospect of the research on self-tuning regulators.Journal of System Science and Mathematical,32:1460–1471,2012.
[2]Z.Z.Yuan,R.Y.Ruan.Application of Modern Control Theory in Engineering.Beijing:Science Press,1985,chapter 5.
[3]K.J.strm,B.Wittenmark.On self-tuning regulators.Automatica,9:185C199,1973.
[4]L.Guo,H.F.Chen.The?Astrm-Wittenmark self-tuning regulator revisited and ELS based adaptive tracker.IEEE Transactions on Automatic Control,36:802–812,1991.
[5]L.Guo.Convergence and logarithm law of self-tuning regulators.Automatica,31:435C450,1995.
[6]R.F.Engle.Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation.Econometrica,50:987–1007,1982.
[7]T.P.Bollerslev.Generalized autoregressive conditional heteroskedasticity.Journal of Econometrics,31:307–327,1986.
[8]C.Z.Sun,H.Z.An,G.F.Wu.Issues on ARCH model,its applications and some developments.Mathematical Statistics and Applied Probability,10(4):62–70,1995.
[9]R.F.Engle.The use of ARCH/GARCH models in applied econometrics.Journal of Economic Perspectives,15:157–168,2001.
[10]Chow,C.Gregory.Analysis and Control of Dynamic Economic Systems.New York:John Wiley and Sons,1975.
[11]D.Hamilton.Time Series Analysis.New Jersey:Princeton University Press,1994,chapter 21.
[12]G.C.Goodwin,K.S.Sin.Adaptive Filtering,Prediction and Control.New Jersey:Prentice-Hall.1984.
[13]L.Guo,D.Z.Cheng,D.X.Feng.Introduction to Control Theory.Beijing:Science Press,2005,chapter 9.
1there exist constants C>C>0 such that C<1/nn∑ i=1w2i
[2]Z.Z.Yuan,R.Y.Ruan.Application of Modern Control Theory in Engineering.Beijing:Science Press,1985,chapter 5.
[3]K.J.strm,B.Wittenmark.On self-tuning regulators.Automatica,9:185C199,1973.
[4]L.Guo,H.F.Chen.The?Astrm-Wittenmark self-tuning regulator revisited and ELS based adaptive tracker.IEEE Transactions on Automatic Control,36:802–812,1991.
[5]L.Guo.Convergence and logarithm law of self-tuning regulators.Automatica,31:435C450,1995.
[6]R.F.Engle.Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation.Econometrica,50:987–1007,1982.
[7]T.P.Bollerslev.Generalized autoregressive conditional heteroskedasticity.Journal of Econometrics,31:307–327,1986.
[8]C.Z.Sun,H.Z.An,G.F.Wu.Issues on ARCH model,its applications and some developments.Mathematical Statistics and Applied Probability,10(4):62–70,1995.
[9]R.F.Engle.The use of ARCH/GARCH models in applied econometrics.Journal of Economic Perspectives,15:157–168,2001.
[10]Chow,C.Gregory.Analysis and Control of Dynamic Economic Systems.New York:John Wiley and Sons,1975.
[11]D.Hamilton.Time Series Analysis.New Jersey:Princeton University Press,1994,chapter 21.
[12]G.C.Goodwin,K.S.Sin.Adaptive Filtering,Prediction and Control.New Jersey:Prentice-Hall.1984.
[13]L.Guo,D.Z.Cheng,D.X.Feng.Introduction to Control Theory.Beijing:Science Press,2005,chapter 9.
1there exist constants C>C>0 such that C<1/nn∑ i=1w2i