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ABSTRACT: This article reviews the development of experiment design in the field of identification of dynamical systems, from the early work of the seventies on input design for open loop identification to the developments of the last decade that were spurred by the research on identification for control. While the early work focused entirely on criteria based on the asymptotic parameter covariance, the results of the last decade aim at minimizing a wide range of possible criteria, including measures of the estimated transfer function, or of functions of this estimated transfer function.
Two important recent developments are the solution of the experiment design problem for closed loop identification, and the formulation and solution of the dual optimal design problem in which the cost of identification is minimized subject to a quality constraint on the estimated model. We shall conclude this survey with new results on the optimal closed loop experiment design problem, where the optimization is performed jointly with respect to the controller and the spectrum of the external excitation.
Communications in information and systems. 01/2011; 11(3):197-224.
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Automatica. 01/2010; 46:577-584.
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Proceedings of the 48th IEEE Conference on Decision and Control, CDC 2009, combined withe the 28th Chinese Control Conference, December 16-18, 2009, Shanghai, China; 01/2009
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ABSTRACT: Within a stochastic noise framework, the validation of a model yields an ellipsoidal parameter uncertainty set, from which
a corresponding uncertainty set can be constructed in the space of transfer functions. We display the role of the experimental
conditions used for validation on the shape of this validated set, and we connect a measure of the size of this set to the
stability margin of a controller designed from the nominal model. This allows one to check stability robustness for the validated
model set and to propose guidelines for validation design.
03/2007: pages 72-86;
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Automatica. 01/2006; 42:1651-1662.
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Automatica. 01/2003; 39:417-427.
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Automatica. 01/2003; 39:403-415.
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ABSTRACT: . Within as tochas ic nois framework, the validation of a model yields an ellipsli al parameter uncertaintys5 , from which acorres onding uncertainty s et can be cons tructed in thes pace of trans fer functions . We dis play the role of the experimental conditions us5 for validation on the s ape of this validated sB , and we connect a meas re of thes ize of this s et to thes tability margin of a controller desFW ed from the nominal model. This allows one to check s ability robus tnes for the validated models et and to propos guidelines for validation desFW . 1
06/2001;
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ABSTRACT: This paper presents a coherent framework for model validation for control and for controller validation (for stability and for performance) in the context where the validated model uncertainty sets are obtained by prediction error identification methods. Thus, these uncertainty sets are parametrized transfer function sets, with parameters lying in ellipsoidal regions in parameter space. Our results cover two distinct aspects: (1) Control-oriented model validation results, where we show that a measure of size of the validated model set is connected to the size of the model-based controller set that robustly stabilizes the model set, leading to validation design guidelines. (2) Controller validation results, where we present necessary and sufficient conditions for a controller to stabilize all models, or to achieve a given level of performance for all models, in such uncertainty set.
03/2000;
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ABSTRACT: First principles models are commonly obtained using finite element or finite difference methods. One of the advantages of these models is that the states in the model have a clear physical interpretation. This makes of them perfect candidates for the monitoring of the states of the system. Unfortunately, the CPU time associated with each evaluation of these complex models is often far too large for these models to be used for online monitoring purposes. This paper introduces a general method to approximate a computationally expensive first principles model with a quasi-linear parameter varying (q-LPV) model. Besides approximating the original model accurately and conserving the physical interpretation of the states, the resulting q-LPV model has generally a much simpler structure than the original model. This in turn implies that the CPU time associated with each model evaluation is generally considerably reduced, allowing the use of these models for online monitoring. Unlike other q-LPV identification techniques, the proposed method extensively uses the availability of the original first principles model.
Journal of Process Control.
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ABSTRACT: This paper presents a new controller validation method for linear multivariable time-invariant models. Classical prediction error system identification methods deliver uncertainty regions which are nonstandard in the robust control literature. Our controller validation criterion computes an upper bound for the worst case performance, measured in terms of the H∞-norm of a weighted closed loop transfer matrix, achieved by a given controller over all plants in such uncertainty sets. This upper bound on the worst case performance is computed via an LMI-based optimization problem and is deduced via the separation of graph framework. Our main technical contribution is to derive, within that framework, a very general parametrization for the set of multipliers corresponding to the nonstandard uncertainty regions resulting from PE identification of MIMO systems. The proposed approach also allows for iterative experiment design. The results of this paper are asymptotic in the data length and it is assumed that the model structure is flexible enough to capture the true system.
Automatica.
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ABSTRACT: We propose a model validation procedure that consists of a prediction error identification experiment with a full order model. It delivers a parametric uncertainty ellipsoid and a corresponding set of parameterized transfer functions, which we call prediction error (PE) uncertainty set. Such uncertainty set differs from the classical uncertainty descriptions used in robust control analysis and design. We develop a robust control analysis theory for such uncertainty sets, which covers two distinct aspects: (1) Controller validation. We present necessary and sufficient conditions for a specific controller to stabilize—or to achieve a given level of performance with—all systems in such PE uncertainty set. (2) Model validation for robust control. We present a measure for the size of such PE uncertainty set that is directly connected to the size of a set controllers that stabilize all systems in the model uncertainty set. This allows us to establish that one uncertainty set is better tuned for robust control design than another, leading to control-oriented validation objectives.
Automatica.
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ABSTRACT: In this paper we briefly review the evolution of the main tools and results for optimal experiment design for system identification. The initial work dates back to the seventies and focused on the accuracy of the parameters of the input-output transfer function estimate. In the eighties, new formulas for the variance of transfer function estimates based on high-order model approximations led to the first goal-oriented experiment design results. The recent trend is to address control-oriented optimal design questions using the more accurate parameter covariance formulas for finite order models.
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ABSTRACT: The purpose of this paper is to evaluate the relia-bility and finite sample properties of different likelihood based methods for constructing probabilistic parameter confidence regions in prediction error identification using ARX (Auto Regression with eXogenous inputs) models. The paper presents alternatives for the "classical" approach to constructing prob-abilistic confidence regions in prediction error identification.
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ABSTRACT: This paper focuses on the validation of a controller designed from a model validated in an ellipsoidal uncertainty set. A controller is said to be validated if it stabilizes all models in this uncertainty set. This set is embedded in a coprime factor uncertainty set in order to use the results of mainstream robust control theory such as the Vinnicombe gap between plants and the related stability theorems.
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ABSTRACT: The purpose of this paper is to evaluate the reliability in finite samples of different methods for constructing probabilistic parameter confidence regions in prediction error identification using Output Error (OE) models. The paper presents alternatives to the "classical method" of constructing asymptotically valid confidence regions, which is based on the asymptotic statistical properties of the parameter estimator. It is shown that if alternative test statistics are used, more reliable confidence regions for finite samples can be obtained. Particularly, it is demonstrated that the use of a test statistic based on the Fisher score allows the construction of exact confidence regions for finite samples.
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ABSTRACT: A problem when designing Kalman filters using first principles models is often that these models lack a description of the noises that affect the states and the measurements. In these cases, the Kalman filter has to be estimated from data. For this purpose many algorithms have been presented in the literature. All methods in the literature assume that the system under consideration has an observability matrix that has no small singular values. In this paper it will be shown that small singular values can lead to poor performance of estimated Kalman filters. Also a method will be introduced for estimating the Kalman filter in the case that the system has small singular values. This method is able to construct a good filter, even if the first principles model is badly observable. Copyright c 2005 IFAC.
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[show abstract]
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ABSTRACT: We propose a model validation procedure that consists of a prediction error iden- tication experiment with a full order model. It delivers a parametric uncertainty ellipsoid and a corresponding set of parametrized transfer functions, which we call PE (for Prediction Error) uncertainty set. Such uncertainty set diers from the clas- sical uncertainty descriptions used in robust control analysis and design. We develop a robust control analysis theory for such uncertainty sets, which covers two distinct aspects. (1) Controller validation. We present necessary and sucien t conditions for a specic controller to stabilize - or to achieve a given level of performance with - all systems in such PE uncertainty set. (2) Model validation for robust control. We present a measure for the size of such PE uncertainty set that is directly connected to the size of a set controllers that stabilize all systems in the model uncertainty set. This allows us to establish that one uncertainty set is better tuned for robust control design than another, leading to control-oriented validation objectives.
