| 1. |
- Annergren, Mariette
(författare)
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ADMM for l1 Regularized Optimization Problems and Applications Oriented Input Design for MPC
- 2012
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)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. |
- Hägg, Per
(författare)
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On Structured System Identification and Nonparametric Frequency Response Estimation
- 2014
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- To keep up with the ever increasing demand on performance and efficiency of control systems, accurate models are needed. System identification is concerned with the estimation and validation of mathematical models of dynamical systems from experimental data. The main problem considered in this thesis is how to take advantage of structural information in system identification. Including this additional information can significantly improve the quality of the identified model.First, the problem of input design for networked systems is considered. Results from closed-loop input design are generalized to the networked case. The main difference between the networked setting and the classical open- or closed-loop setting is the possibility of using measurable, or known, disturbances to improve the excitation. Such disturbances cannot be affected during the experiment and are common in industrial applications.A framework to include the additional information about the measurable disturbances in the input design is presented. The framework is evaluated in two simulation examples and several interesting observations are made.Second, the result from an input design is often the correlation properties of the input signal.The question is then how to generate the input signal that can be applied to the system with the given properties. This thesis presents a novel signal generation method that is able to handle input and output constraints. In industrial applications, it is often vital to satisfy constraints on both the input and the output signals during the system identification experiment. The method is formulated as a reference tracking Model Predictive Controller (MPC), with the desired correlation properties of the signal as reference, while satisfying the input and output constraints on the considered system. The core of the algorithm is the formulation of the signal generation as an MPC which allows the use existing tools to make the algorithm robust and adaptive. The proposed method is evaluated in several simulation studies and successfully applied to a physical lab process.Third, nonparametric estimates of the frequency response function of a system are used in almost all engineering fields. The final contribution of this thesis is to present a novel nonparametric method, called the Transient and Impulse Response Modeling Method (TRIMM). The method is inspired by the local polynomial method, but uses more information about the known structure of the leakage error in the estimation of the frequency response. The bias and variance errors of TRIMM are analyzed and the results are used to connect system properties and the choice of user parameters with the performance of the method. The analysis can also be used to compare the performance of different methods and to give guidelines to the user on how to choose method.
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| 3. |
- Hägg, Per
(författare)
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Using Structural Information in System Identification
- 2012
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Recent advances in small and cheap communication and sensing have opened up for large scale systems with intricate interconnections and interactions. These applications pose new challenges for analysis and control design. To keep up with the increasing demand on performance and efficiency, accurate models of these systems are needed. Often some prior knowledge of the system, such as system structure, is available.Prior knowledge should whenever possible be used in system identification to improve the model estimate.This thesis addresses the problem of using prior information about the overall structure of the system in system identification. Two special structures are considered, the cascade and the parallel serial structure. The motivation for looking at these structures are two folded; they are common in industrial applications and they can be used to build up almost all interesting feedforward interconnected systems. The effect of sensor placement, input signals and common dynamics of the subsystems on the quality of the estimated models for these two structures is considered.In many control applications it is vital that the model has a physical interpretation. Hence, it is important that the system identification method retains the physical interpretation of the identified model. However, it has proven hard to incorporate prior knowledge of structure in subspace methods. This thesis presents two methods for identifying systems with known structures using subspace methods. The first method utilizes that the state-space matrices of a system on cascade form have a certain structure. The idea is to find a transform that takes the identified system back to this form. The second method uses the known structure of the extended observability matrix. The state-space matrices for the subsystems can then be found by solving linear least squares problems. However, the method is only applicable if the second subsystem has order one. But this is a common case in practice. The two methods are applied to a two tank lab process with promising results.Nonparametric estimates of the frequency response function of systems are used in most engineering fields. The second contribution of this thesis is a new method for estimating the frequency response. The method uses the known structure of the transient or leakage error. The feasibility of the method is tested in simulations. For the two cases considered, one with a large amount of random systems, the second with a resonant system, the method shows good performance compared to current state of the art methods.
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| 4. |
- Ohlsson, Henrik, 1981-
(författare)
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Regularization for Sparseness and Smoothness : Applications in System Identification and Signal Processing
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In system identification, the Akaike Information Criterion (AIC) is a well known method to balance the model fit against model complexity. Regularization here acts as a price on model complexity. In statistics and machine learning, regularization has gained popularity due to modeling methods such as Support Vector Machines (SVM), ridge regression and lasso. But also when using a Bayesian approach to modeling, regularization often implicitly shows up and can be associated with the prior knowledge. Regularization has also had a great impact on many applications, and very much so in clinical imaging. In e.g., breast cancer imaging, the number of sensors is physically restricted which leads to long scantimes. Regularization and sparsity can be used to reduce that. In Magnetic Resonance Imaging (MRI), the number of scans is physically limited and to obtain high resolution images, regularization plays an important role.Regularization shows-up in a variety of different situations and is a well known technique to handle ill-posed problems and to control for overfit. We focus on the use of regularization to obtain sparseness and smoothness and discuss novel developments relevant to system identification and signal processing.In regularization for sparsity a quantity is forced to contain elements equal to zero, or to be sparse. The quantity could e.g., be the regression parameter vectorof a linear regression model and regularization would then result in a tool for variable selection. Sparsity has had a huge impact on neighboring disciplines, such as machine learning and signal processing, but rather limited effect on system identification. One of the major contributions of this thesis is therefore the new developments in system identification using sparsity. In particular, a novel method for the estimation of segmented ARX models using regularization for sparsity is presented. A technique for piecewise-affine system identification is also elaborated on as well as several novel applications in signal processing. Another property that regularization can be used to impose is smoothness. To require the relation between regressors and predictions to be a smooth function is a way to control for overfit. We are here particularly interested in regression problems with regressors constrained to limited regions in the regressor-space e.g., a manifold. For this type of systems we develop a new regression technique, Weight Determination by Manifold Regularization (WDMR). WDMR is inspired byapplications in biology and developments in manifold learning and uses regularization for smoothness to obtain smooth estimates. The use of regularization for smoothness in linear system identification is also discussed.The thesis also presents a real-time functional Magnetic Resonance Imaging (fMRI) bio-feedback setup. The setup has served as proof of concept and been the foundation for several real-time fMRI studies.
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