| 1. |
- Malmström, Magnus, 1994-
(författare)
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Uncertainties in Neural Networks : A System Identification Approach
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In science, technology, and engineering, creating models of the environment to predict future events has always been a key component. The models could be everything from how the friction of a tire depends on the wheels slip to how a pathogen is spread throughout society. As more data becomes available, the use of data-driven black-box models becomes more attractive. In many areas they have shown promising results, but for them to be used widespread in safety-critical applications such as autonomous driving some notion of uncertainty in the prediction is required.An example of such a black-box model is neural networks (NNs). This thesis aims to increase the usefulness of NNs by presenting an method where uncertainty in the prediction is obtained by linearization of the model. In system identification and sensor fusion, under the condition that the model structure is identifiable, this is a commonly used approach to get uncertainty in the prediction from a nonlinear model. If the model structure is not identifiable, such as for NNs, the ambiguities that cause this have to be taken care of in order to make the approach applicable. This is handled in the first part of the thesis where NNs are analyzed from a system identification perspective, and sources of uncertainty are discussed.Another problem with data-driven black-box models is that it is difficult to know how flexible the model needs to be in order to correctly model the true system. One solution to this problem is to use a model that is more flexible than necessary to make sure that the model is flexible enough. But how would that extra flexibility affect the uncertainty in the prediction? This is handled in the later part of the thesis where it is shown that the uncertainty in the prediction is bounded from below by the uncertainty in the prediction of the model with lowest flexibility required for representing true system accurately. In the literature, many other approaches to handle the uncertainty in predictions by NNs have been suggested, of which some are summarized in this work. Furthermore, a simulation and an experimental studies inspired by autonomous driving are conducted. In the simulation study, different sources of uncertainty are investigated, as well as how large the uncertainty in the predictions by NNs are in areas without training data. In the experimental study, the uncertainty in predictions done by different models are investigated. The results show that, compared to existing methods, the linearization method produces similar results for the uncertainty in predictions by NNs.An introduction video is available at https://youtu.be/O4ZcUTGXFN0
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| 2. |
- Annergren, Mariette, 1982-
(författare)
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Application-Oriented Input Design and Optimization Methods Involving ADMM
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is divided into two main parts. The first part considers application-oriented input design, specifically for model predictive control (MPC). The second part considers alternating direction method of multipliers (ADMM) for ℓ1 regularized optimization problems and primal-dual interior-point methods.The theory of system identification provides methods for estimating models of dynamical systems from experimental data. This thesis is focused on identifying models used for control, with special attention to MPC. The objective is to minimize the cost of the identification experiment while guaranteeing, with high probability, that the obtained model gives an acceptable control performance. We use application-oriented input design to find such a model. We present a general procedure of implementing application-oriented input design to unknown, possibly nonlinear, systems controlled using MPC. The practical aspects of application-oriented input design are addressed and the method is tested in an experimental study.In addition, a MATLAB-based toolbox for solving application-oriented input design problems is presented. The purpose of the toolbox is threefold: it is used in research; it facilitates communication of research results; it helps an engineer to use application-oriented input design.Several important problems in science can be formulated as convex optimization problems. As such, there exist very efficient algorithms for finding the solutions. We are interested in methods that can handle optimization problems with a very large number of variables. 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, and ℓ1 regularized MPC. The former occurs in signal processing and the latter is a specific type of model based control.We are also interested in optimization problems with certain structural limitations. These limitations inhibit the use of a central computational unit to solve the problems. We derive a distributed method for solving them instead. The method is a primal-dual interior-point method that uses ADMM to distribute all the calculations necessary to solve the optimization problem at hand.
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| 3. |
- Barenthin Syberg, Märta, 1979-
(författare)
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Complexity Issues, Validation and Input Design for Control in System Identification
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification is about constructing and validating modelsfrom measured data. When designing system identificationexperiments in control applications, there are many aspects toconsider. One important aspect is the choice of model structure.Another crucial issue is the design of input signals. Once a modelof the system has been estimated, it is essential to validate theclosed loop performance if the feedback controller is based onthis model. In this thesis we consider the prediction-erroridentification method. We study model structure complexity issues,input design and model validation for control. To describe real-life systems with high accuracy, models of veryhigh complexity are typically needed. However, the variance of themodel estimate usually increases with the model order. In thisthesis we investigate why system identification, despite thisrather pessimistic observation, is successfully applied in theindustrial practise as a reliable modelling tool. It is shown thatby designing suitable input signals for the identificationexperiment, we obtain accurate estimates of the frequency functionalso for very complex systems. The input power spectrum can beused to shape the model quality. A key tool in input design is tointroduce a linear parametrization of the spectrum. With thisparametrization, several optimal input design problems can berewritten as convex optimization problems. Another problem considered is to design controllers withguaranteed robust stability and prescribed robust performanceusing models identified from experimental data. These models areuncertain due to process noise, measurement noise and unmodelleddynamics. In this thesis we only consider errors due tomeasurement noise. The model uncertainty is represented byellipsoidal confidence regions in the model parameter space. Wedevelop tools to cope with these ellipsoids for scalar andmultivariable models. These tools are used for designing robustcontrollers, for validating the closed loop performance and forimproving the model with input design. Therefore this thesis ispart of the research effort to connect prediction-erroridentification methods and robust control theory. The stability of the closed loop system can be validated using thesmall gain theorem. A critical issue is thus to have an accurateestimate of the L2-gain of the system. The key tosolve this problem is to find the input signal that maximizes thegain. One approach is to use a model of the system to design theinput signal. An alternative approach is to let the system itselfdetermine a suitable input sequence in repeated experiments. Insuch an approach no model of the system is required. Proceduresfor gain estimation of linear and nonlinear systems are discussedand compared.
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| 4. |
- Ljungberg, Fredrik, 1993-
(författare)
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Estimation of Nonlinear Greybox Models for Marine Applications
- 2020
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- As marine vessels are becoming increasingly autonomous, having accurate simulation models available is turning into an absolute necessity. This holds both for facilitation of development and for achieving satisfactory model-based control. When accurate ship models are sought, it is necessary to account for nonlinear hydrodynamic effects and to deal with environmental disturbances in a correct way. In this thesis, parameter estimators for nonlinear regression models where the regressors are second-order modulus functions are analyzed. This model class is referred to as second-order modulus models and is often used for greybox identification of marine vessels. The primary focus in the thesis is to find consistent estimators and for this an instrumental variable (IV) method is used.First, it is demonstrated that the accuracy of an IV estimator can be improved by conducting experiments where the input signal has a static offset of sufficient amplitude and the instruments are forced to have zero mean. This two-step procedure is shown to give consistent estimators for second-order modulus models in cases where an off-the-shelf applied IV method does not, in particular when measurement uncertainty is taken into account.Moreover, it is shown that the possibility of obtaining consistent parameter estimators for models of this type depends on how process disturbances enter the system and on the amount of prior knowledge about the disturbances’ probability distributions that is available. In cases where the first-order moments are known, the aforementioned approach gives consistent estimators even when disturbances enter the system before the nonlinearity. In order to obtain consistent estimators in cases where the first-order moments are unknown, a framework for estimating the first and second-order moments alongside the model parameters is suggested. The idea is to describe the environmental disturbances as stationary stochastic processes in an inertial frame and to utilize the fact that their effect on a vessel depends on the vessel’s attitude. It is consequently possible to infer information about the environmental disturbances by over time measuring the orientation of a vessel they are affecting. Furthermore, in cases where the process disturbances are of more general character it is shown that supplementary disturbance measurements can be used for achieving consistency.Different scenarios where consistency can be achieved for instrumental variable estimators of second-order modulus models are demonstrated, both in theory and by simulation examples. Finally, estimation results obtained using data from a full-scale marine vessel are presented.
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| 5. |
- Müller, Matias I.
(författare)
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Learning Sequential Decision Rules in Control Design: Regret-Optimal and Risk-Coherent Methods
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Engineering sciences deal with the problem of optimal design in the face of uncertainty. In particular, control engineering is concerned about designing policies/laws/algorithms that sequentially take decisions given unreliable data. This thesis addresses two particular instances of optimal sequential decision making for two different problems.The first problem is known as the H∞-norm (or, in general, ℓ2-gain for nonlinear systems) estimation problem, which is a fundamental quantity in control design through, e.g., the small gain theorem. Given an unknown system, the goal is to find the maximum ℓ2-gain which, in a model-free approach, involves solving a sequential input design problem. The H∞-norm estimation problem (or simply "gain estimation problem") is cast as the composition of multi-armed bandit problem generating data, and an optimal estimation problem given that data. The problem of generating data is a sequential input-design problem in which, at every round, the decision-maker chooses one (or many) frequencies to sample from the unknown frequency response of the system under study. We show that Thompson Sampling (TS), a classical bandit algorithm, is optimal within the class of algorithms that chooses only one frequency per round. Additionally, we introduce Weighted Thompson Sampling (WTS), which is a TS-based algorithm that can sample many frequencies at every round. In this thesis, we prove that WTS is an optimal bandit policy within the class of algorithms that can sample many frequencies simultaneously. On the other hand, the problem of estimating the H∞-norm of the system using the data provided by the bandit algorithm is also discussed. In particular, we show that the expected estimation error of the gain of the system asymptotically matches the Cramér-Rao lower bound for a proposed estimator, and for every bandit policy in a wide class of algorithms.In the second part, we address the problem of risk-coherent optimal control design for disturbance rejection under uncertainty, where optimality is studied from an H2 and an H∞ sense. We consider a parametric model for the plant and the noise spectrum, where the modeling error between the model and the real system is uncertain. This uncertainty is condensed in a probability density function over the different realizations of the parameters defining the model. We use this information to design a controller that minimizes the risk of falling into poor closed-loop performance within a financial theory of risk framework. When the parameters in the plant are not known with sufficient accuracy for control purposes, we introduce a framework that allows us to tackle the joint-stabilization problem by means of sequential convex relaxations, each of them leading to a semi-definite program. On the other hand, when the noise spectrum is uncertain, we propose a systematic scenario approach for designing H2- and H∞-optimal controllers in terms of quadratically-constrained linear programs and sequential semi-definite programming, respectively. Simulations show that, from a risk-theoretical perspective, exploiting the information encoded in the probability density function of the parameters defining the models better balances the risk of falling into poor closed-loop performances.
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| 6. |
- Abdalmoaty, Mohamed, 1986-
(författare)
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Learning Stochastic Nonlinear Dynamical Systems Using Non-stationary Linear Predictors
- 2017
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The estimation problem of stochastic nonlinear parametric models is recognized to be very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the maximum likelihood estimator and the optimal mean-square error predictor using Monte Carlo methods. Albeit asymptotically optimal, these methods come with several computational challenges and fundamental limitations.The contributions of this thesis can be divided into two main parts. In the first part, approximate solutions to the maximum likelihood problem are explored. Both analytical and numerical approaches, based on the expectation-maximization algorithm and the quasi-Newton algorithm, are considered. While analytic approximations are difficult to analyze, asymptotic guarantees can be established for methods based on Monte Carlo approximations. Yet, Monte Carlo methods come with their own computational difficulties; sampling in high-dimensional spaces requires an efficient proposal distribution to reduce the number of required samples to a reasonable value.In the second part, relatively simple prediction error method estimators are proposed. They are based on non-stationary one-step ahead predictors which are linear in the observed outputs, but are nonlinear in the (assumed known) input. These predictors rely only on the first two moments of the model and the computation of the likelihood function is not required. Consequently, the resulting estimators are defined via analytically tractable objective functions in several relevant cases. It is shown that, under mild assumptions, the estimators are consistent and asymptotically normal. In cases where the first two moments are analytically intractable due to the complexity of the model, it is possible to resort to vanilla Monte Carlo approximations. Several numerical examples demonstrate a good performance of the suggested estimators in several cases that are usually considered challenging.
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| 7. |
- Ebadat, Afrooz, 1986-
(författare)
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Experiment Design for Closed-loop System Identification with Applications in Model Predictive Control and Occupancy Estimation
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The objective of this thesis is to develop algorithms for application-oriented input design. This procedure takes the model application into account when designing experiments for system identification.This thesis is divided into two parts. The first part considers the theory of application-oriented input design, with special attention to Model Predictive Control (MPC). We start by studying how to find a convex approximation of the set of models that result in acceptable control performance using analytical methods when controllers with no closed-form control law, for e.g., MPC are employed. The application-oriented input design is formulated in time domain to enable handling of signals constraints. The framework is extended to closed-loop systems where two cases are considered i.e., when the plant is controlled by a general but known controller and for the case of MPC. To this end, an external stationary signal is designed via graph theory. Different sources of uncertainty in application-oriented input design are investigated and a robust application-oriented input design framework is proposed.The second part of this thesis is devoted to the problem of estimating the number of occupants based on the information available to HVAC systems in buildings. The occupancy estimation is first formulated as a two-tier problem. In the first tier, the room dynamic is identified using temporary measurements of occupancy. In the second tier, the identified model is employed to formulate the problem as a fused-lasso problem. The proposed method is further developed to be used as a multi-room estimator using a physics-based model. However, since it is not always possible to collect measurements of occupancy, we proceed by proposing a blind identification algorithm which estimates the room dynamic and occupancy, simultaneously. Finally, the application-oriented input design framework is employed to collect data that is informative enough for occupancy estimation purposes.
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| 8. |
- Kreiberg, David, 1971-
(författare)
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A covariance structure analysis approach to the errors-in-variables estimation problem
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- It is a well-known fact that standard regression techniques, when applied to errors-in-variables (EIV) models, lead to biased and inconsistent parameter estimation. The work presented in this thesis address the EIV estimation problem using covariance structure analysis (CSA). When performing CSA, the standard implementation of the minimum distance (MD) estimator is to apply computationally demanding nonlinear least squares (NLLS). This thesis provides a solution to this problem by proposing a computationally less demanding separable nonlinear least squares (SNLLS) implementation of the estimator.The thesis consists of four papers. The first paper presents a covariance matching (CM) approach for identifying the single-input single-output (SISO) EIV model. The outlined approach extends previous known results by deriving an asymptotic covariance matrix of the jointly estimated system parameters, noise variances and auxiliary parameters. The second paper introduces two formulations of the SISO EIV model using structural equation modeling (SEM). The two formulations allow for quick implementation using standard SEM-based software. The third paper propose a numerically more efficient implementation of the MD estimator for estimating confirmatory factor analysis (CFA) models. The implementation uses an SNLLS approach, which allows part of the parameter vector to be estimated using numerically efficient linear techniques. The fourth and final paper presents a CFA-EIV modeling approach that allows for colored output noise. The presentation extends previous work by including a detailed treatment of the theoretical aspects of the MD estimator. All four papers use simulation examples to illustrate the outlined procedures.
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| 9. |
- Larsson, Christian A., 1983-
(författare)
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Application-oriented experiment design for industrial model predictive control
- 2014
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Advanced process control and its prevalent enabling technology, model predictive control (MPC), can today be regarded as the industry best practice for optimizing production. The strength of MPC comes from the ability to predict the impact of disturbances and counteract their effects with control actions, and from the ability to account for constraints. These capabilities come from the use of models of the controlled process. However, relying on a model is also a weakness of MPC.The model used by the controller needs to be kept up to date with changing process conditions for good MPC performance. In this thesis, the problem of closed-loop system identification of models intended to be used in MPC is considered.The design of the identification experiment influences the quality and properties of the estimated model. In the thesis, an application-oriented framework for designing the identification experiment is used. The specifics of experiment design for identification of models for MPC are discussed. In particular, including constraints in the controllerresults in a nonlinear control law, which complicates the experiment design.The application-oriented experiment design problem with time-domain constraints is formulated as an optimal control problem, which in general is diffcult to solve. Using Markov decision theory, the experiment design problem is formulated for finite state and action spaces and solved using an extension of existing linear programming techniques for constrained Markov decision processes. The method applies to general noise and disturbance structures but is computationally intensive. Two extensions of MPC with dual control properties which implement the application-oriented experiment design idea are developed. These controllers are limited to output error systems but require less computations. Furthermore, since the controllers are based on a common MPC technique, they can be used as extensions of already available MPC implementations. One of the developed controllers is tested in an extensive experimental validation campaign, which is the first time that MPC with dual propertiesis applied to a full scale industrial process during regular operation of the plant.Existing experiment design procedures are most often formulated in the frequency domain and the spectrum of the input is used as the design variable. Therefore, a realization of the signal with the right spectrum has to be generated. This is not straightforward for systems operating under constraints. In the thesis, a framework for generating signals, with prespecified spectral properties, that respect system constraints is developed. The framework uses ideas from stochastic MPC and scenario optimization. Convergence to the desired autocorrelation is proved for a special case and the merits of the algorithm are illustrated in a series of simulation examples.
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| 10. |
- Parsa, Javad
(författare)
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Estimation and optimal input design in sparse models
- 2023
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Sparse parameter estimation is an important aspect of system identification, as it allows for reducing the order of a model, and also some models in system identification inherently exhibit sparsity in their parameters. The accuracy of the estimated sparse model depends directly on the performance of the sparse estimation methods. It is well known that the accuracy of a sparse estimation method relies on the correlations between the regressors of the model being estimated. Mutual coherence represents the maximum of these correlations. When the parameter vector is known to be sparse, accurate estimation requires a low mutual coherence.However, in system identification, a major challenge arises from the construction of the regressor based on time series data, which often leads to a high mutual coherence. This conflict hinders accurate sparse estimation. To address this issue, the first part of this thesis introduces novel methods that reduce mutual coherence through linear coordinate transformations. These methods can be integrated with any sparse estimation techniques. Our numerical studies demonstrate significant improvements in performance compared to state-of-the-art sparse estimation algorithms.In the second part of the thesis, we shift our focus to optimal input design in system identification, which aims to achieve maximum accuracy in a model based on specific criteria. The original optimal input design techniques lack coherence constraints between the input sequences, often resulting in high mutual coherence and, consequently, increased sparse estimation errors for sparse models. Therefore, the second part of the thesis concentrates on designing optimal input for sparse models. We formulate the proposed methods and propose numerical algorithms using alternating minimization. Additionally, we compare the performance of our proposed methods with state-of-the-art input design algorithms, and we provide theoretical analysis of the proposed methods in both parts of the thesis.
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