| 1. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Identification of Stochastic Nonlinear Models Using Optimal Estimating Functions
- 2020
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 119
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Tidskriftsartikel (refereegranskat)abstract
- The first part of the paper examines the asymptotic properties of linear prediction error method estimators, which were recently suggested for the identification of nonlinear stochastic dynamical models. It is shown that their accuracy depends not only on the shape of the unknown distribution of the data, but also on how the model is parameterized. Therefore, it is not obvious in general which linear prediction error method should be preferred. In the second part, the estimating functions approach is introduced and used to construct estimators that are asymptotically optimal with respect to a specific class of estimators. These estimators rely on a partial probabilistic parametric models, and therefore neither require the computations of the likelihood function nor any marginalization integrals. The convergence and consistency of the proposed estimators are established under standard regularity and identifiability assumptions akin to those of prediction error methods. The paper is concluded by several numerical simulation examples.
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| 2. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
-
Linear Prediction Error Methods for Stochastic Nonlinear Models
- 2019
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 105, s. 49-63
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Tidskriftsartikel (refereegranskat)abstract
- The estimation problem for stochastic parametric nonlinear dynamical models is recognized to be challenging. The main difficulty is the intractability of the likelihood function and the optimal one-step ahead predictor. In this paper, we present relatively simple prediction error methods based on non-stationary predictors that are linear in the outputs. They can be seen as extensions of the linear identification methods for the case where the hypothesized model is stochastic and nonlinear. The resulting estimators are defined by analytically tractable objective functions in several common cases. It is shown that, under certain identifiability and standard regularity conditions, the estimators are consistent and asymptotically normal. We discuss the relationship between the suggested estimators and those based on second-order equivalent models as well as the maximum likelihood method. The paper is concluded with a numerical simulation example as well as a real-data benchmark problem.
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| 3. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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On Re-Weighting, Regularization Selection, and Transient in Nuclear Norm Based Identification
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 48:28, s. 92-97
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Tidskriftsartikel (refereegranskat)abstract
- In this contribution, we consider the classical problem of estimating an Output Error model given a set of input-output measurements. First, we develop a regularization method based on the re-weighted nuclear norm heuristic. We show that the re-weighting improves the estimate in terms of better fit. Second, we suggest an implementation method that helps in eliminating the regularization parameters from the problem by introducing a constant based on a validation criterion. Finally, we develop a method for considering the effect of the transient when the initial conditions are unknown. A simple numerical example is used to demonstrate the proposed method in comparison to classical and another recent method based on the nuclear norm heuristic.
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| 4. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(författare)
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Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem⁎
- 2018
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Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 784-789
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Tidskriftsartikel (refereegranskat)abstract
- The estimation problem of stochastic Wiener-Hammerstein models is recognized to be challenging, mainly due to the analytical intractability of the likelihood function. In this contribution, we apply a computationally attractive prediction error method estimator to a real-data stochastic Wiener-Hammerstein benchmark problem. The estimator is defined using a deterministic predictor that is nonlinear in the input. The prediction error method results in tractable expressions, and Monte Carlo approximations are not necessary. This allows us to tackle several issues considered challenging from the perspective of the current mainstream approach. Under mild conditions, the estimator can be shown to be consistent and asymptotically normal. The results of the method applied to the benchmark data are presented and discussed.
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| 5. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(författare)
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Identification of a Class of Nonlinear Dynamical Networks⁎
- 2018
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Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 868-873
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Tidskriftsartikel (refereegranskat)abstract
- Identification of dynamic networks has attracted considerable interest recently. So far the main focus has been on linear time-invariant networks. Meanwhile, most real-life systems exhibit nonlinear behaviors; consider, for example, two stochastic linear time-invariant systems connected in series, each of which has a nonlinearity at its output. The estimation problem in this case is recognized to be challenging, due to the analytical intractability of both the likelihood function and the optimal one-step ahead predictors of the measured nodes. In this contribution, we introduce a relatively simple prediction error method that may be used for the estimation of nonlinear dynamical networks. The estimator is defined using a deterministic predictor that is nonlinear in the known signals. The estimation problem can be defined using closed-form analytical expressions in several non-trivial cases, and Monte Carlo approximations are not necessarily required. We show, that this is the case for some block-oriented networks with no feedback loops and where all the nonlinear modules are polynomials. Consequently, the proposed method can be applied in situations considered challenging by current approaches. The performance of the estimation method is illustrated on a numerical simulation example.
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| 6. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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The Gaussian MLE versus the Optimally weighted LSE
- 2020
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Ingår i: IEEE signal processing magazine (Print). - : Institute of Electrical and Electronics Engineers (IEEE). - 1053-5888 .- 1558-0792. ; 37:6, s. 195-199
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Tidskriftsartikel (refereegranskat)abstract
- In this note, we derive and compare the asymptotic covariance matrices of two parametric estimators: the Gaussian Maximum Likelihood Estimator (MLE), and the optimally weighted Least-Squares Estimator (LSE). We assume a general model parameterization where the model's mean and variance are jointly parameterized, and consider Gaussian and non-Gaussian data distributions.
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| 7. |
- Agüero, Juan C., et al.
(författare)
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Accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation
- 2012
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 48:4, s. 632-637
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study the accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation. We present a frequency-domain representation for the information matrix for general linear MIMO models. We show that the variance of estimated parametric models for linear MIMO systems satisfies a fundamental integral trade-off. This trade-off is expressed as a multivariable 'water-bed' effect. An extension to spectral estimation is also discussed.
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| 8. |
- Akcay, H., et al.
(författare)
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On the choice of norms in system identification
- 1996
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Ingår i: IEEE Transactions on Automatic Control. - Linköping : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286. ; 41:9, s. 1367-1372
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Tidskriftsartikel (refereegranskat)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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| 9. |
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| 10. |
- Barenthin, Märta, et al.
(författare)
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Identification and control: Joint input design and H-infinity state feedback with ellipsoidal parametric uncertainty via LMIs
- 2008
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 44:2, s. 543-551
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Tidskriftsartikel (refereegranskat)abstract
- One obstacle in connecting robust control with models generated from prediction error identification is that very few control design methods are able to directly cope with the ellipsoidal parametric uncertainty regions that are generated by such identification methods. In this contribution we present a joint robust state feedback control/input design procedure which guarantees stability and prescribed closed-loop performance using models identified from experimental data. This means that given H-infinity specifications on the closed-loop transfer function are translated into sufficient requirements on the input signal spectrum used to identify the process. The condition takes the form of a linear matrix inequality.
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