Consistent parameter bounding identification for linearly parametrized model sets

Hakvoort, R.G.; Hof, Paul M.J. Van den

doi:10.1016/0005-1098(95)00173-t

Cited by 32 publications

(17 citation statements)

References 15 publications

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“…By the strong law of large numbers, ξ N → ξ = F(C 2n(m+1) − Φθ ; α), w.p.1 as N → ∞ (11) for some (2n(m + 1)) × n Toeplitz matrix Φ. Partition Φ into 2(m + 1) submatrices of dimension n × n, Φ = ⎡…”

Section: B Sufficient Excitation Conditionsmentioning

confidence: 99%

“…There are numerous textbooks and monographs on the subject in a stochastic or worst-case framework, such as [10], [15], [16]. Many significant results have been obtained for identification and adaptive control involving random disturbances in the past decades [2], [11], [14], [10], [15]. The utility of set-valued observations carries a flavor that is related to many branches of signal processing problems.…”

Section: Introductionmentioning

confidence: 99%

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Sufficient excitation conditions for system identification using binary-valued observations

Wang

Yin²,

Zhao

et al. 2006

2006 American Control Conference

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Conditions on input signals are derived that characterize their probing richness for system identification using binary-valued observations. Identification configurations in open-loop, filtering, and feedback systems are discussed together with different scenarios of noises including actuator noise, input measurement noise, and output measurement noises. In addition to system parameter estimation, identifiability and sufficient excitation conditions are also derived under unknown threshold and noise distributions.

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Section: B Sufficient Excitation Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sufficient excitation conditions for system identification using binary-valued observations

Wang

Yin²,

Zhao

et al. 2006

2006 American Control Conference

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“…The set of unfalsified models is given by (8) A related quantity of interest, often, is the size of the set and is computed by (9) where . We will refer to as the diameter of uncertainty at time .…”

Section: Problem Formulationmentioning

confidence: 99%

“…If the source of corrup-0018-9286/97$10.00 © 1997 IEEE tion is noise, we model it by imposing temporal constraints on the possible realizations of noise. Related work on imposing such restrictions has been carried out in [1] and [9]. On the other hand, if it results from unmodeled dynamics, then informational constraints are imposed.…”

Section: Introductionmentioning

confidence: 99%

Identification in the presence of classes of unmodeled dynamics and noise

Venkatesh

Dahleh

1997

IEEE Trans. Automat. Contr.

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Identification involves obtaining a model from an a priori chosen model class(es) using finite corrupted data. The corruption may be due to several reasons ranging from noise to unmodeled dynamics, since the real system may not belong to the model class. Two popular approaches-probabilistic and setmembership identification-deal with this problem by imposing temporal constraints on the noise sample paths. We differentiate between the two sources of error by imposing different types of constraints on the corruption. If the source of corruption is noise, we model it by imposing temporal constraints on the possible realizations of noise. On the other hand, if it results from unmodeled dynamics informational constraints are imposed.Contrary to probabilistic identification where the parameters of the identified model converge to the true parameters in the presence of noise, current results in set-membership identification do not have this convergence property. Our approach leads to bridging this gap between probabilistic and set-membership identification when the source of corruption is noise. For the case when both unmodeled dynamics and noise are present, we derive consistency results for the case when the unmodeled dynamics can be described either by an linear time-invariant system or by a static nonlinearity.

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“…A unified methodology which combines worst case identification and probability framework was recently introduced in [32]. The issues of estimation consistency in worst case identification were treated by Kakvoort and Van den Hof [14] in which main ideas from probability frameworks were extended to set-membership descriptions for disturbances.…”

Section: Introductionmentioning

confidence: 99%

Persistent identification of systems with unmodeled dynamics and exogenous disturbances

Wang

Yin

2000

IEEE Trans. Automat. Contr.

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In this paper, a novel framework of system identification is introduced to capture the hybrid features of systems subject to both deterministic unmodeled dynamics and stochastic observation disturbances. Using the concepts of persistent identification, control-oriented system modeling, and stochastic analysis, we investigate the central issues of irreducible identification errors and time complexity in such identification problems. Upper and lower bounds on errors and speed of persistent identification are obtained. The error bounds are expressed as functions of observation lengths, sizes of unmodeled dynamics, and probability distributions of disturbances. Asymptotic normality and complexity lower bounds are investigated when periodic inputs and LS estimation are applied. Generic features of asymptotic normality are further explored to extend the asymptotic lower bounds to a wider range of signals and identification mappings.

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Consistent parameter bounding identification for linearly parametrized model sets

Cited by 32 publications

References 15 publications

Sufficient excitation conditions for system identification using binary-valued observations

Sufficient excitation conditions for system identification using binary-valued observations

Identification in the presence of classes of unmodeled dynamics and noise

Persistent identification of systems with unmodeled dynamics and exogenous disturbances

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