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Optimal average case estimation in Hilbert norms

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS 2000年第4期13卷 347-359页

作者： Kacewicz, B Stanislaw Staszic Univ Min & Met Dept Appl Math PL-30059 Krakow Poland

In contrast to the worst case approach, the average case setting provides less conservative insight into the quality of estimation algorithms. In this paper we consider two local average case error measures of algorithms based on noisy information, in Hilbert norms in the problem element and information spaces. We define the optimal algorithm and provide formulas for its two local errors, which explicitly exhibit the influence of factors such as information, information (measurement) errors, norms in the considered spaces, a subset where approximations are allowed, and "unmodeled dynamics." Based on the error expression, we formulate in algebraic language the problem of selecting the optimal approximating subspace. The solution is given along with the specific formula for the error, which depends on the eigenvalues of a certain matrix defined by information and norms under consideration.

关键词： identification algorithms average case setting local errors optimal algorithm optimal subspace

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Optimally conditioned instrumental variable approach for frequency-domain system identification

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AUTOMATICA 2014年第9期50卷 2281-2293页

作者： van Herpen, Robbert Oomen, Tom Steinbuch, Maarten Eindhoven Univ Technol NL-5600 MB Eindhoven Netherlands Eindhoven Univ Technol Dept Mech Engn Control Syst Technol Grp NL-5600 MB Eindhoven Netherlands

Accurate frequency-domain system identification demands for reliable computational algorithms. The aim of this paper is to develop a new algorithm for parametric system identification with favorable convergence properties and optimal numerical conditioning. Recent results in frequency-domain instrumental variable identification are exploited, which lead to enhanced convergence properties compared to classical identification algorithms. In addition, bi-orthonormal polynomials with respect to a data-dependent bi-linear form are introduced for system identification. Hereby, optimal numerical conditioning of the relevant system of equations is achieved. This is shown to be particularly important for the class of instrumental variable algorithms, for which numerical conditioning is typically quadratic compared to alternative frequency-domain identification algorithms. Superiority of the proposed algorithm is demonstrated by means of both simulation and experimental results. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： System identification identification algorithms Numerical methods Matrix inversion Condition numbers

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An output error recursive algorithm for unbiased identification in closed loop

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AUTOMATICA 1997年第5期33卷 933-938页

作者： Landau, ID Karimi, A Lab. d'Automatique de Grenoble ENSIEG 38402 Saint Martin d'Hères BP 46 France

The problem of unbiased recursive identification of a plant model in closed-loop operation is considered. A particular form of an output error predictor for the closed loop is introduced. This allows one to derive a parameter estimation algorithm for the plant model that is globally asymptotically stable and asymptotically unbiased in the presence of noise. The paper presents a stability analysis in a deterministic environment and a convergence analysis in the stochastic environment. Both require a mild sufficient passivity condition to be satisfied. Simulations and real-time experiments on flexible transmission illustrate the performances of the proposed algorithm. (C) 1997 Elsevier Science Ltd.

关键词： identification algorithms output-error identification stability analysis convergence analysis passivity

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A matrix nullspace approach for solving equality-constrained multivariable polynomial least-squares problems

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AUTOMATICA 2014年第12期50卷 3030-3037页

作者： Hoelze, Matthew S. Bernstein, Dennis S. Univ Bremen Parallel Comp Embedded Sensor Syst Res Grp D-28359 Bremen Germany German Aerosp Ctr DLR D-28359 Bremen Germany Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA

We present an elimination theory-based method for solving equality-constrained multivariable polynomial least-squares problems in system identification. While most algorithms in elimination theory rely upon Groebner bases and symbolic multivariable polynomial division algorithms, we present an algorithm which is based on computing the nullspace of a large sparse matrix and the zeros of a scalar, univariate polynomial. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： identification algorithms Least squares Multivariable polynomial

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DESIGN CRITERIA FOR ROBUST STRICT POSITIVE REALNESS IN ADAPTIVE SCHEMES

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AUTOMATICA 1994年第4期30卷 643-654页

作者： TESI, A VICINO, A ZAPPA, G UNIV SIENA FAC INGNI-53100 SIENAITALY

Design of filters ensuring convergence of recursive estimation algorithms in the presence of uncertainty in the plant model is a key problem in the area of identification and adaptive control. This paper addresses the problem of designing filters ensuring strict positive realness of a family of uncertain polynomials over an assigned region of the complex plane. The uncertainty is assumed to be both structured and unstructured. When the structured uncertainty of the family is represented through regions of root location of a certain shape (for instance, circles centered on the real axis), an optimal solution of the problem is provided. For more general uncertainty regions, a simple procedure for constructing sub-optimal solutions to the filter design problem is proposed. A numerical example is fully developed to show the effectiveness of the proposed approach.

关键词： STRICT POSITIVE REALNESS UNCERTAIN POLYNOMIALS FILTER DESIGN identification algorithms ADAPTIVE CONTROL

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identification of the unobservable behaviour of industrial automation systems by Petri nets

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CONTROL ENGINEERING PRACTICE 2011年第9期19卷 958-966页

作者： Dotoli, Mariagrazia Fanti, Maria Pia Mangini, Agostino M. Ukovich, Walter Politecn Bari Dipartimento Elettrotecn & Elett Bari Italy Univ Trieste Dipartimento Elettrotecn Elett & Informat Trieste Italy

This paper addresses the problem of identifying the model of the unobservable behaviour of discrete event systems in the industrial automation sector. Assuming that the fault-free system structure and dynamics are known, the paper proposes an algorithm that monitors the system on-line, storing the occurred observable event sequence and the corresponding reached states. At each event observation, the algorithm checks whether some unobservable events have occurred on the basis of the knowledge of the Petri net (PN) modelling the nominal system behaviour and the knowledge of the current PN marking. By defining and solving some integer linear programming problems, the algorithm decides whether it is necessary to introduce some unobservable (silent) transitions in the PN model and provides a PN structure that is consistent with the observed event string. A case study describing an industrial automation system shows the efficiency and the applicability of the proposed algorithm. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Industrial automation systems Discrete event systems Petri nets identification algorithms Integer programming Modelling

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Estimating models with high-order noise dynamics using semi-parametric weighted null-space fitting

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AUTOMATICA 2019年 102卷 45-57页

作者： Galrinho, Miguel Rojas, Cristian R. Hjalmarsson, Hakan KTH Royal Inst Technol Sch Elect Engn & Data Sci Dept Automat Control SE-10044 Stockholm Sweden

Standard system identification methods often provide inconsistent estimates with closed-loop data. With the prediction error method (PEM), this issue is solved by using a noise model that is flexible enough to capture the noise spectrum. However, a too flexible noise model (i.e., too many parameters) increases the model complexity, which can cause additional numerical problems for PEM. In this paper, we consider the weighted null-space fitting (WNSF) method. With this method, the system is first modeled using a non-parametric ARX model, which is then reduced to a parametric model of interest using weighted least squares. In the reduction step, a parametric noise model does not need to be estimated if it is not of interest. Because the flexibility of the noise model is increased with the sample size, this will still provide consistent estimates in closed loop and asymptotically efficient estimates in open loop. In this paper, we prove these results, and we derive the asymptotic covariance for the estimation error obtained in closed loop, which is optimal for an infinite-order noise model. For this purpose, we also derive a new technical result for geometric variance analysis, instrumental to our end. Finally, we perform a simulation study to illustrate the benefits of the method when the noise model cannot be parametrized by a low-order model. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： System identification Closed-loop identification Non-parametric identification Parameter identification identification algorithms Least squares

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Recursive 4SID algorithms using gradient type subspace tracking

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AUTOMATICA 2002年第6期38卷 1035-1043页

作者： Oku, H Kimura, H Univ Twente Fac Appl Phys Syst & Control Engn Div NL-7500 AE Enschede Netherlands Univ Tokyo Grad Sch Frontier Sci Dept Complex Sci & Engn Bunkyo Ku Tokyo 1138656 Japan

Sometimes we obtain some prior information about a system to be identified, e.g., the order, model structure etc. In this paper, we consider the case where the order of a MIMO system to be identified is a priori known. Recursive subspace state-space system identification algorithms presented here are based on the gradient type subspace tracking method used in the array signal processing. The algorithms enable us to estimate directly the subspace spanned by the column vectors of the extended observability matrix of the system to be identified without performing the singular value decomposition. Also, a new convergence proof of the gradient type subspace tracking is given in this paper. Under the condition of a step size between 0 and 1, we prove the convergence property of the recursive equation of the gradient type subspace tracking. A numerical example illustrates that our algorithm is more robust with respect to the choice of the initial values than the corresponding PAST one. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： identification algorithms subspace methods gradient methods convergence proofs matrix inversion adaptive filters

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On indirect identification of feedback-control systems via the instrumental variables methods

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS 2003年第9期50卷 1232-1238页

作者： Zheng, WX Univ Western Sydney Sch Quantitat Methods & Math Sci Penrith NSW 1797 Australia

Indirect closed-loop identification assumes the knowledge of the controller. In this brief, the constrained version of the instrumental variable (IV) methods is developed. It is based on using the known controller parameters to impose linear constraints upon the closed-loop system parameters and then solving the constrained estimation problem by the La-grange method. The developed constrained IV methods outperform the unconstrained counterparts in, such aspects as insensitivity to common factors, estimation accuracy and robustness against noise. Computer simulations are presented which not only support the theoretical analysis, but also give good insight into the properties of the developed constrained IV methods.

关键词： constrained optimization feedb.ack-control systems identification algorithms parameter estimation

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identification of positive linear systems with Poisson output transformation

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AUTOMATICA 2002年第5期38卷 861-868页

作者： De Santis, A Farina, L Dipartimento Informat & Sistemat A Ruberti I-00184 Rome Italy

We study the identification problem for third-order linear time invariant positive systems in experiments where the output is a Poisson process. The problem well-posedness is investigated when the input-output model is described by a sum of real exponentials. A maximum likelihood procedure is then proposed and the admissible set for the unknown parameters is characterized. The novelty of the approach consists in solving a constrained maximum likelihood problem to estimate residues and eigenvalues based on theoretical results on minimality of positive realizations recently obtained in the literature. Numerical results are also provided. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： positive systems positive realization identification algorithms Poisson processes pharmacokinetics network traffic analysis

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