The Dead Zone in System Identification

K. Forsman and L. Ljung
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K. Forsman: ABB Corporate Research, Ideon
L. Ljung: Linköping University, Department of Electrical Engineering

Chapter 5 in Bounding Approaches to System Identification, 1996, pp 69-82 from Springer

Abstract: Abstract A prediction error method for parameter estimation in a dynamical system is studied. % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacuaHrpGsgaqcaiabg2da9iGacggacaGGYbGaai4za8aacaaMh8+a % aCbeaeaapeGaciyBaiaacMgacaGGUbaal8aabaWdbiabeg9akbWdae % qaaOWaaCbeaeaapeGaciiBaiaacMgacaGGTbaal8aabaWdbiaad6ea % cqGHsgIRcqGHEisPa8aabeaak8qadaWcaaWdaeaapeGaaGymaaWdae % aapeGaamOtaaaadaaeWbWdaeaapeGaaeyraiaadYgadaqadaWdaeaa % peGaeqyTdu2aaeWaa8aabaWdbiaadshacaGGSaGaeqy0dOeacaGLOa % GaayzkaaaacaGLOaGaayzkaaaal8aabaWdbiaadshacqGH9aqpcaaI % Xaaapaqaa8qacaWGobaaniabggHiLdaaaa!5BCF! $$ \hat \vartheta = \arg {\mkern 1mu} \mathop {\min }\limits_\vartheta \mathop {\lim }\limits_{N \to \infty } \frac{1}{N}\sum\limits_{t = 1}^N {{\text{E}}l\left( {\varepsilon \left( {t,\vartheta } \right)} \right)} $$ where ε are the prediction errors of a linear regression. A quadratic norm l is zero within an interval [−c, c]. This kind of a dead zone (DZ) criterion is very common in robust adaptive control. The following problems are treated in this chapter: When is the DZ estimate inconsistent, and what is the set of parameters which minimizes the criterion in the case of inconsistency? What happens to the variance of the estimate as the DZ is introduced? Does the DZ give a better estimate than least squares (LS) when there are unmodeled deterministic disturbances present? What are the relations between identification with a dead zone criterion and so called set membership identification?

Keywords: Dead Zone; Little Square Estimate; Asymptotic Covariance Matrix; Adaptive Regulator; Robust Adaptive Control (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-1-4757-9545-5_5

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