为了解决生产过程的计算机控制问题,首先要解决系统的模型辨识问题.由于计算机的普遍使用,提出了许多适时的递推辨识方法[1,2].因此下面两个问题很自然地引起普遍关注:1.递推算法是否收敛?2.即使递推算法收敛了,还有一致性问题,也就是它是否收敛到真值.
Abstract
In this paper a general recursive algorithm of stochastic type is considered when the dynamic noise is the martineale difference sequence.The sufficient conditions for its convergence and consistency are given and proved to be capable of being essentially weakened to guarantee the consistency only if the algorithm is known as convergent.It is shown that for a specific class of algorithms including the least squares the consistency conditions can be further simplified.
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参考文献
[1] G.C.Ooodwin and R.L.Payne,Dynamic System Identification: Experiment Design and Data Analysis,Academic Press,New York,1977.
[2] P.Eykhoff,System Identification,Wiley,New York,1974.
[3] L.Ljung,Analysis of Recursive stochastic Algorithms,IEEE Tran,a.AC-22:4(7977),551-575.
[4] —.Consistency of the Least Squares Identification Method.IEFF.Traps.AC-21:5(1976),779-781.
[5] J.B.Moore and B.D.O.Anderson,On Martingalea and Least Squares Linear System Identification,Dep.Elec.Eng.Univ.Newea.atle,NSW,Australia,Tech,Rep.EE 7522.1975.
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[7] A.Dvoretzky,On Stochastic Approximation,Proe.3rd Berkeley Syp.Math.Stat.Prob.,1,1956.
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[10] G.R.Hardy,J.E.Littlewood and G.Polya,Inequalities,Cambridge University Press,London,1934.
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脚注
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