| 1. |
- Godoy, B. I., et al.
(författare)
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A novel input design approach for systems with quantized output data
- 2014
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Ingår i: 2014 European Control Conference, ECC. - : IEEE. - 9783952426913 ; , s. 1049-1054
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Konferensbidrag (refereegranskat)abstract
- In this paper, we explore the problem of input design for systems with quantized measurements. For the input design problem, we calculate and optimize a function of the Fisher Information Matrix (FIM). The calculation of the FIM is greatly simplified by using known relationships of the derivative of the likelihood function, and the auxiliary function arising from the Expectation Maximization (EM) algorithm. To optimize the FIM, we design an experiment using a recently published method based on graph theory. A numerical example shows that the proposed experiment can be successfully used in quantized systems.
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| 2. |
- Bottegal, G., et al.
(författare)
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On maximum likelihood identification of errors-in-variables models
- 2017
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 50:1, s. 2824-2829
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we revisit maximum likelihood methods for identification of errors-in-variables systems. We assume that the system admits a parametric description, and that the input is a stochastic ARMA process. The cost function associated with the maximum likelihood criterion is minimized by introducing a new iterative solution scheme based on the expectation-maximization method, which proves fast and easily implementable. Numerical simulations show the effectiveness of the proposed method.
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| 3. |
- Courts, Jarrad, et al.
(författare)
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Variational State and Parameter Estimation
- 2021
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Ingår i: IFAC PapersOnLine. - : Elsevier. - 2405-8963. ; , s. 732-737
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Konferensbidrag (refereegranskat)abstract
- This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this work, a variational approach is used to provide an assumed density which approximates the desired, intractable, distribution. The approach is deterministic and results in an optimisation problem of a standard form. Due to the parametrisation of the assumed density selected first- and second-order derivatives are readily available which allows for efficient solutions. The proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in two numerical examples.
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| 4. |
- Courts, Jarrad, et al.
(författare)
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Variational system identification for nonlinear state-space models
- 2023
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 147
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has deep connections to maximum likelihood estimation. This VI approach ultimately provides estimates of the model as solutions to an optimisation problem, which is deterministic, tractable and can be solved using standard optimisation tools. A specialisation of this approach for systems with additive Gaussian noise is also detailed. The proposed method is examined numerically on a range of simulated and real examples focusing on the robustness to parameter initialisation; additionally, favourable comparisons are performed against state-of-the-art alternatives.
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| 5. |
- Geng, Li-Hui, et al.
(författare)
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Smoothed State Estimation via Efficient Solution of Linear Equations
- 2017
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Ingår i: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963. ; 50:1, s. 1613-1618
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Tidskriftsartikel (refereegranskat)abstract
- This paper addresses the problem of computing fixed interval smoothed state estimates of a linear time varying Gaussian stochastic system. There already exist many algorithms that perform this computation, but all of them impose certain restrictions on system matrices in order for them to be applicable. This paper develops a new forwards–backwards pass algorithm that is applicable under the mildest restrictions possible - namely that the smoothed state distribtions exists in forms that can be characterised by means and covariances, for which this paper also develops a new necessary and sufficient condition.
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| 6. |
- Hendriks, Johannes N., et al.
(författare)
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Data to Controller for Nonlinear Systems : An Approximate Solution
- 2022
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Ingår i: IEEE Control Systems Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 2475-1456. ; 6, s. 1196-1201
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Tidskriftsartikel (refereegranskat)abstract
- This letter considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modeled by a nonlinear state-space model, but where the model parameters, state and future disturbances are not known and are treated as random variables. Central to our formulation is that the joint distribution of these unknown objects is conditioned on the observed data. Crucially, as new measurements become available, this joint distribution continues to evolve so that control decisions are made accounting for uncertainty as evidenced in the data. The resulting problem is intractable which we obviate by providing approximations that result in finite dimensional deterministic optimization problems. The proposed approach is demonstrated in simulation on a nonlinear system.
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| 7. |
- Hjalmarsson, Håkan, 1962-, et al.
(författare)
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Least-squares estimation of a class of frequency functions : A finite sample variance expression
- 2006
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 42:4, s. 589-600
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Tidskriftsartikel (refereegranskat)abstract
- A new expression for the variance of scalar frequency functions estimated using the least-squares method is presented. The expression is valid for finite sample size and for a class of model structures, which includes finite impulse response, Laguerre and Kautz models, when the number of estimated parameters coincides with the number of excitation frequencies of the input. The expression gives direct insight into how excitation frequencies and amplitudes affect the accuracy of frequency function estimates. With the help of this expression, a severe sensitivity of the accuracy with respect to the excitation frequencies is exposed. The relevance of the expression when more excitation frequencies are used is also discussed.
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| 8. |
- Ninness, B., et al.
(författare)
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Analysis of the variability of joint input-output estimation methods
- 2005
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 41:7, s. 1123-1132
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Tidskriftsartikel (refereegranskat)abstract
- It has been recently established that, when estimating parametric models on the basis of closed loop data, the frequency domain variability of direct and various indirect methods may significantly differ from one another. This paper continues this work by analysing the performance of certain common joint input-output estimation methods.
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| 9. |
- Ninness, B., et al.
(författare)
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Model structure and numerical properties of normal equations
- 2001
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Ingår i: IEEE Transactions on Circuits And Systems Part I. - : Institute of Electrical and Electronics Engineers (IEEE). - 1057-7122 .- 1558-1268. ; 48:4, s. 425-437
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Tidskriftsartikel (refereegranskat)abstract
- There has been recent interest in using ortho-normalized forms of fixed denominator model structures for system identification, A key motivating factor in the employment of these forms is that of improved numerical properties. Namely, for white input, perfect conditioning of the least-squares normal equations is achieved by design. However, for the more usual case of colored input spectrum, it is not clear what the numerical conditioning properties should be in relation to simpler and perhaps more natural model structures. This paper provides theoretical and empirical evidence to argue that in fact, even though the orthonormal structures are only designed to provide perfect numerical conditioning for white input, they still provide improved conditioning for a wide variety of colored inputs.
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| 10. |
- Ninness, B., et al.
(författare)
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On the Frequency Domain Accuracy of Closed Loop Estimates
- 2003
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Ingår i: Proceedings of the IEEE Conference on Decision and Control. - 0780379241 ; , s. 5997-6002
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Konferensbidrag (refereegranskat)abstract
- It has been argued that the frequency domain accuracy of high model-order estimates obtained on the basis of closed loop data is largely invariant to whether direct or indirect approaches are used. This paper revisits this study in light of new variance quantification results that apply for low model order and establishes that, under certain assumptions, there can be significant differences in the accuracy of frequency response estimates that are dependent on what type of direct, indirect or joint input-output identification strategy is pursued.
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