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- Akcay, H., et al.
(author)
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On the choice of norms in system identification
- 1996
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In: IEEE Transactions on Automatic Control. - Linköping : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286. ; 41:9, s. 1367-1372
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Journal article (peer-reviewed)abstract
- In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C > 0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all ℓp-norms, p ≀ 2 < ∞ for F(C). ©1996 IEEE.
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- Gustafsson, Fredrik, et al.
(author)
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Twenty-one ML estimators for model selection
- 1995
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In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 31:10, s. 1377-1392
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Journal article (peer-reviewed)abstract
- Classical approaches to determine a suitable model structure from observed input-output data are based on hypothesis tests and information-based criteria. Recently, the model structure has been considered as a stochastic variable, and standard estimation techniques have been proposed. The resulting estimators are closely related to the aforementioned methods. However, it turns out that there are a number of prior choices in the problem formulation, which are crucial for the estimators' behavior. The contribution of this paper is to clarify the role of the prior choices, to examine a number of possibilities and to show which estimators are consistent. This is done in a linear regression framework. For autoregressive models, we also investigate a novel prior assumption on stability, and give the estimator for the model order and the parameters themselves. Copyright © 1995 Elsevier Science Ltd All rights reserved.
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- Hjalmarsson, Håkan, 1962-, et al.
(author)
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Composite modeling of transfer functions
- 1995
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In: Proceedings of the IEEE Conference on Decision and Control. - New Orleans, LA, USA : Institute of Electrical and Electronics Engineers (IEEE). - 0780326857 ; 40:5, s. 820-832
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Conference paper (peer-reviewed)abstract
- The problem under consideration is how to estimate the frequency function of a system and the associated estimation error when a set of possible model structures is given and when one of them is known to contain the true system. The 'classical' solution to this problem is to, firstly, use a consistent model structure selection criterium to discard all but one single structure. Secondly, estimate a model in this structure and, thirdly, conditioned on the assumption that the chosen structure contains the true system, compute an estimate of the estimation error. However, for a finite data set one cannot guarantee that the correct structure is chosen and this 'structural' uncertainty is lost in the previously mentioned approach. In this contribution a method is developed that combines the frequency function estimates and the estimation errors from all possible structures into a joint estimate and estimation error. Hence, this approach by-passes the structure selection problem. This is accomplished by employing a Bayesian setting.
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- Hjalmarsson, Håkan, 1962-
(author)
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Efficient tuning of linear multivariable controllers using iterative feedback tuning
- 1999
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In: International journal of adaptive control and signal processing (Print). - 0890-6327 .- 1099-1115. ; 13:7, s. 553-572
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Journal article (peer-reviewed)abstract
- Iterative feedback tuning is a direct tuning method using closed-loop experimental data. The method is based on numerical optimization and in each iteration an unbiased gradient estimate is used. Due to these unbiased gradient estimates, the method converges to a stationary point of the control criterion provided the closed loop signals remain bounded throughout the iterations. In this contribution, it is shown how such unbiased estimates can be obtained for multivariable linear time-invariant systems. Particular attention is given to the issue of keeping the experiment time to a minimum and several efficient algorithms are presented. It is shown that, for tuning an arbitrary linear time-invariant multivariable controller with nw inputs and nu outputs, 1+nu×nw experiments are sufficient in each iteration of the algorithm. For disturbance rejection, an alternative algorithm is proposed which requires nu+nw experiments. As an illustration, the method is applied to a simulation model of a gas turbine engine.
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- Hjalmarsson, Håkan, 1962-, et al.
(author)
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Fast, non-iterative estimation of Hidden Markov models
- 1998
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In: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. - Seattler, WA, USA. ; , s. 2253-2256
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Conference paper (peer-reviewed)abstract
- The solution of many important signal processing problems depends on the estimation of the parameters of a Hidden Markov Model (HMM). Unfortunately, to date the only known methods for performing this estimation have been iterative, and therefore computationally demanding. By way of contrast, this paper presents a new fast and non-iterative method that utilizes certain recent 'state spaced subspace system identification' (4SID) ideas from the control theory literature. A short simulation example presented here indicates this new technique to be almost as accurate as Maximum-Likelihood estimation, but an order of magnitude less computationally demanding than the Baum-Welch (EM) algorithm.
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8. |
- Hjalmarsson, Håkan, 1962-, et al.
(author)
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For model-based control design, closed-loop identification gives better performance
- 1996
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In: Automatica. - 0005-1098. ; 32:12, s. 1659-1673
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Journal article (peer-reviewed)abstract
- We compare open loop versus closed loop identification when the identified model is used for control design, and when the system itself belongs to the model class, so that only variance errors are relevant. Our measure of controller performance (which is used as our design criterion for identification) is the variance of the error between the output of the ideal closed loop system (with the ideal controller) and that of the actual closed loop system (with the controller computed from the identified model). Under those conditions, we show that, when the controller is a smooth function of the input-output dynamics and the disturbance spectrum, the best controller performance is achieved by performing the identification in closed loop with an operating controller that we characterize. For minimum variance and model reference control design cirteria, we show that this 'optimal operating controller for identification' is the ideal controller. This then leads to a suboptimal but feasible iterative scheme. Copyright © 1996 Elsevier Science Ltd.
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- Hjalmarsson, Håkan, 1962-, et al.
(author)
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Identification in closed loop : Asymptotic high order variance for restricted complexity models
- 1998
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Conference paper (peer-reviewed)abstract
- Asymptotic high order variance expressions for identified models have found widespread use in e.g. optimal experiment design, analysis of model accuracy and control. The expressions derived in the 1970's and 1980's by Berk, Ljung and others are valid for a wide range of operating conditions and models such as restricted complexity models identified from open loop data as well as full order models identified from closed loop data. Throughout the 1990's much attention has been devoted to the issue of identification of models based on closed loop data. In order to, at least asymptotically in the model order, be able to analyze the quality of such models a corresponding high order variance theory for restricted complexity models identified from closed loop data is necessary. This paper provides this for models with a fixed noise model. A novel variance expression, valid for Gaussian signals, is derived. Simulations show that this expression is surprisingly accurate also for non-Gaussian signals.
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