| 1. |
- Annergren, Mariette
(author)
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ADMM for l1 Regularized Optimization Problems and Applications Oriented Input Design for MPC
- 2012
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Licentiate thesis (other academic/artistic)abstract
- This licentiate thesis is divided into two main parts. The first part considers alternating direction method of multipliers (ADMM) for ℓ1 regularized optimization problems and the second part considers applications oriented input design for model predictive control (MPC).Many important problems in science and engineering can be formulated as convex optimization problems. As such, they have a unique solution and there exist very efficient algorithms for finding the solution. We are interested in methods that can handle big, in terms of the number of variables, optimization problems in an efficient way. Large optimization problems are common in many fields of research, for example, the problem of feature selection from huge medical data sets. ADMM is a method capable of handling such problems. We derive a scalable and efficient algorithm based on ADMM for two ℓ1 regularized optimization problems: ℓ1 mean and covariance filtering that occur in signal processing, and ℓ1 regularized MPC that is a specific type of model based control.System identification provides tools for estimating models of dynamical systems from experimental data. The application of such models can be divided into three main categories: prediction, simulation and control. We focus on identifying models used for control, with special attention to MPC. The objective is to minimize a cost related to the identification experiment while guaranteeing, with high probability, that the obtained model gives an acceptable control performance. We use applications oriented input design to find such a model. We present a general procedure of implementing applications oriented input design to unknown, and possibly nonlinear, systems controlled using MPC. In addition, we show that the input design problem obtained for output-error systems has the same simple structure as for finite impulse response systems.
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| 2. |
- Bauer, Dietmar, et al.
(author)
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Asymptotic properties of Hammerstein model estimates
- 2000
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In: Proceedings of the 39th IEEE Conference on Decision and Control. - 0780366387
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Conference paper (peer-reviewed)abstract
- This paper considers the estimation of Hammerstein models with input saturation. These models are characterised by a linear dynamical model acting on an input sequence which is affected by a hard saturation of unknown level. The main result of the paper lies in a specication of a set of sufficient conditions on the input sequence in order to ensure that a non-linear least-squares approach enjoys properties of consistency and asymptotic normality and furthermore, that an estimate of the parameter covariance matrix is also consistent. The set of assumptions is specied using the concept of near epoch dependence, which has been developed in the econometrics literature. Indeed, one purpose of this paper is to highlight the usefulness of this concept in the context of analysing estimation procedures for nonlinear dynamical systems.
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| 3. |
- Bauer, Dietmar, et al.
(author)
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Asymptotic Properties of Identification of Hammerstein Models with Input Saturation
- 2000
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Reports (other academic/artistic)abstract
- This paper considers the estimation of Hammerstein models with input saturation. These models are characterised by a linear dynamical model acting on an input sequence which is affected by a hard saturation of unknown level. The main result of the paper lies in a specication of a set of sufficient conditions on the input sequence in order to ensure that a non-linear least-squares approach enjoys properties of consistency and asymptotic normality and furthermore, that an estimate of the parameter covariance matrix is also consistent. The set of assumptions is specied using the concept of near epoch dependence, which has been developed in the econometrics literature. Indeed, one purpose of this paper is to highlight the usefulness of this concept in the context of analysing estimation procedures for nonlinear dynamical systems.
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| 4. |
- Courts, Jarrad, et al.
(author)
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Variational State and Parameter Estimation
- 2021
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In: IFAC PapersOnLine. - : Elsevier. - 2405-8963. ; , s. 732-737
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Conference paper (peer-reviewed)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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| 5. |
- Courts, Jarrad, et al.
(author)
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Variational system identification for nonlinear state-space models
- 2023
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In: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 147
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Journal article (peer-reviewed)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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| 6. |
- Geng, Li-Hui, et al.
(author)
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Smoothed State Estimation via Efficient Solution of Linear Equations
- 2017
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In: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963. ; 50:1, s. 1613-1618
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Journal article (peer-reviewed)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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| 7. |
- Geng, Li-Hui, et al.
(author)
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Smoothed State Estimation via Efficient Solution of Linear Equations
- 2023
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In: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523 .- 2334-3303. ; 68:10, s. 5877-5889
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Journal article (peer-reviewed)abstract
- This article 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, and the restrictions vary considerably between the various existing algorithms. This article establishes a new sufficient condition for the fixed-interval smoothing density to exist in a Gaussian form that can be completely characterized by associated means and covariances. It then develops an algorithm to compute these means and covariances with no further assumptions required. This results in an algorithm more generally applicable than any one of the multitude of existing algorithms available to date.
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| 8. |
- Gustafsson, Fredrik, et al.
(author)
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Asymptotic Power and the Benefit of Under-Modeling in Change Detection
- 1995
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In: Proceedings of the 3rd European Control Conference. - Linköping : Linköping University. ; , s. 1237-1242
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Reports (other academic/artistic)abstract
- It is well-known from experience that low order models perform well in change detection problems even if the true system is quite complicated. By computing the asymptotic power function, it is here shown that common hypothesis tests proposed in literature attain their maximum power for a low order model under certain conditions on how much each parameter change.
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| 9. |
- Gustafsson, Fredrik, et al.
(author)
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Asymptotic Power and the Gain of Under-Modelling in Change Detection
- 1994
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Reports (other academic/artistic)abstract
- It is well-known from experience that low order models perform well in change detection problems even if the true system is quite complicated. By computing the asymptotic power function, it is here shown that common hypothesis tests proposed in literature attain their maximum power for a low order model under certain conditions on how much each parameter change.
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| 10. |
- Hendriks, Johannes N., et al.
(author)
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Data to Controller for Nonlinear Systems : An Approximate Solution
- 2022
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In: IEEE Control Systems Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 2475-1456. ; 6, s. 1196-1201
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Journal article (peer-reviewed)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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