A Linear Robustly Convergent Interpolatory Algorithm For System Identification

Set membership H 1 identification is investigated using time-domain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors. The problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error, called radius of information, is solved. For classes of models affine in the parameters, the radius of information is obtained as function of the H1 norm of the unmodeled dynamics. A method is given for estimating this norm from the available data and some general a priori information on the unmodeled dynamics, thus allowing the actual evaluation of the radius of information. The radius represents a measure of the "predictive ability" of the considered class of models, and it is then used for comparing the quality of different classes of models and for the order selection of their parametric part. The effectiveness of the proposed procedure is tested on some numerical examples and compared with standard statistical criteria for model order selection.Index Terms-Identification for robust control, model order selection, set membership identification, uncertainty model identification.

Section: Unmodeled Dynamic Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

H/sub ∞/ identification and model quality evaluation

Giarré

Milanese²,

Taragna³

1997

“…He and coworkers introduced the problem of set-membership identification and produced many interesting results on the subject [20], [19], [21]. Within the framework of -frequency domain identification introduced in [10], many efficient algorithms have been developed, including Bai and Raman [1], Chen et al [3], Gu et al [8], [9], and Makila et al [16], [17].…”

Section: )mentioning

confidence: 99%

“…The norm of is defined by Unstable systems will belong to , the extended space of . 1 The subspace of time invariant systems in will be denoted by . If , its kernel (impulse response) .…”

Section: B Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Persistent identification and adaptation: stabilization of slowly varying systems in H/sup ∞/

Wang

Lin²

1998

In this paper, the problem of persistent identification and adaptive stabilization of time-varying systems is studied within the framework of deterministic worst case identification and slow H 1 adaptation. The plants under consideration are unstable and time-varying and cannot be stabilized by a fixed robust controller. Starting from an initial well-designed operating point, the controller must persistently adapt to the time-varying plant to maintain uniform stability over all future time.A key property which guarantees uniform stability is that the identification-adaptation iteration satisfies a certain invariance principle. We demonstrate that the adaptive design using periodic external inputs, least squares identification, and slow H 1 adaptation possesses such an invariance property, leading to a successful adaptive stabilization methodology. Generic natures of our findings are discussed.

The Caratheodory-Fejer problem and H/sub ∞//l/sub 1/ identification: a time domain approach

Chen

Nett²

1995

Abstruc#-In this paper we study a worse-case, robust control oriented identification problem. This problem is in the framework of H, identification but the formulation here is more general. The available a priori information in our problem consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The plant to be identified is assumed to lie in a certain subset in the space of '&, characterized by the assumed a priori information. The available experimental information consists of a corrupt finite output time series obtained in response to a known nonzero but otherwise arbitrary input. Our objective is to identify from the given U priori and experimental information an uncertain model which consists of a nominal model in H, and a hound on the modeling error measured in 'H , norm. We present both an identification algorithm and several explicit lower and upper bounds on the identification error. The proposed algorithm is in the class of interpolatory algorithms which are known to possess desirable optimality properties in reducing the identification error. This algorithm is obtained by solving an extended Caratheodory-Fejer problem via standard convex programming methods. Both the algorithm and error bounds can be applied to I 1 identification problems as well.