Robust control oriented identification of errors-in-variables models based on normalised coprime factors

J. Control Theory Appl.

Xiao

Zhang

et al. 2011

Self Cite

This paper proposes an L-two-optimal identification approach to cope with errors-in-variables model (EIVM) identification. With normalized coprime factor model (NCFM) representations, L-two-optimal approximate models are derived from the framework of an EIVM according to the kernel and image representations of related signals. Based on the optimal approximate models, the v-gap metric is employed as a minimization criterion to optimize the parameters of a system model, and thus the resulting optimization problem can be solved by linear matrix inequalities (LMIs). In terms of the optimized system model, the noise model (NM) can be readily obtained by right multiplication of an inner. Compared with other EIVM identification methods, the proposed one has a wider scope of applications because the statistical properties of disturbing noises are not demanded. It is also capable of giving identifiability. Finally, a numerical simulation is used to verify the effectiveness of the proposed method.

Section: Optimization Criterionmentioning

confidence: 99%

“…, N ) is the sampled angular frequency. Since P m (λ) is stable from Assumption 1, the point-wise frequency response of G m (λ) can be obtained in the following way [9,14,16]:…”

Section: Optimization Criterionmentioning

confidence: 99%

Section: Optimization Criterionmentioning

confidence: 99%

“…With the aforementioned preparations, an applicable optimization criterion in [14,16] is adopted to optimize the model parameters x n and x d : min…”

Section: Optimization Criterionmentioning

confidence: 99%

“…Notations The notations used in this paper are standard [14][15][16]. Let C denote the set of complex numbers.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

L-two-optimal identification of errors-in-variables models: a frequency-domain approach

J. Control Theory Appl.

Xiao

Zhang

et al. 2011

Self Cite

A convex optimization algorithm for frequency‐domain identification in the v‐gap metric

Adaptive Control & Signal

Cui

et al. 2014

Self Cite

This paper proposes a convex optimization algorithm to minimize the v-gap metric for parameter estimation of a SISO system using frequency-domain measurements. According to a geometrical interpretation for this metric, its evaluation for two SISO linear systems is the supreme of sine values of the apertures between their normalized right graph symbols. As a result, the minimization of the v-gap metric becomes that of the maximum of sine values of those apertures at sampling frequencies and can be efficiently solved by a sequence of feasibility problems with a decreasing line search. Compared with the related algorithms, the proposed one has global convergence and much lower computational loads. Finally, a numerical simulation shows the effectiveness of the proposed algorithm.

Error quantification of the normalized right graph symbol for an errors-in-variables system

Control Theory Technol.

Cui

Xia

2015

This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol (NRGS) for an errorsin-variables (EIV) system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from a priori and a posteriori information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and H ∞ -norm of their NRGSs' difference. The obtained NRGS perturbation model set paves the way for robust controller design using an H ∞ loop-shaping method because it is a standard form of the well-known NCF (normalized coprime factor) perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method.