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  • 1.
    Abdalmoaty, Mohamed
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). KTH Royal Institute of Technology.
    Identification of Stochastic Nonlinear Dynamical Models Using Estimating Functions2019Doctoral thesis, monograph (Other academic)
    Abstract [en]

    Data-driven modeling of stochastic nonlinear systems is recognized as a very challenging problem, even when reduced to a parameter estimation problem. A main difficulty is the intractability of the likelihood function, which renders favored estimation methods, such as the maximum likelihood method, analytically intractable. During the last decade, several numerical methods have been developed to approximately solve the maximum likelihood problem. A class of algorithms that attracted considerable attention is based on sequential Monte Carlo algorithms (also known as particle filters/smoothers) and particle Markov chain Monte Carlo algorithms. These algorithms were able to obtain impressive results on several challenging benchmark problems; however, their application is so far limited to cases where fundamental limitations, such as the sample impoverishment and path degeneracy problems, can be avoided.

    This thesis introduces relatively simple alternative parameter estimation methods that may be used for fairly general stochastic nonlinear dynamical models. They are based on one-step-ahead predictors that are linear in the observed outputs and do not require the computations of the likelihood function. Therefore, the resulting estimators are relatively easy to compute and may be highly competitive in this regard: they are in fact defined by analytically tractable objective functions in several relevant cases. In cases where the predictors are analytically intractable due to the complexity of the model, it is possible to resort to {plain} Monte Carlo approximations. Under certain assumptions on the data and some conditions on the model, the convergence and consistency of the estimators can be established. Several numerical simulation examples and a recent real-data benchmark problem demonstrate a good performance of the proposed method, in several cases that are considered challenging, with a considerable reduction in computational time in comparison with state-of-the-art sequential Monte Carlo implementations of the ML estimator.

    Moreover, we provide some insight into the asymptotic properties of the proposed methods. We show that the accuracy of the estimators depends on the model parameterization and the shape of the unknown distribution of the outputs (via the third and fourth moments). In particular, it is shown that when the model is non-Gaussian, a prediction error method based on the Gaussian assumption is not necessarily more accurate than one based on an optimally weighted parameter-independent quadratic norm. Therefore, it is generally not obvious which method should be used. This result comes in contrast to a current belief in some of the literature on the subject. 

    Furthermore, we introduce the estimating functions approach, which was mainly developed in the statistics literature, as a generalization of the maximum likelihood and prediction error methods. We show how it may be used to systematically define optimal estimators, within a predefined class, using only a partial specification of the probabilistic model. Unless the model is Gaussian, this leads to estimators that are asymptotically uniformly more accurate than linear prediction error methods when quadratic criteria are used. Convergence and consistency are established under standard regularity and identifiability assumptions akin to those of prediction error methods.

    Finally, we consider the problem of closed-loop identification when the system is stochastic and nonlinear. A couple of scenarios given by the assumptions on the disturbances, the measurement noise and the knowledge of the feedback mechanism are considered. They include a challenging case where the feedback mechanism is completely unknown to the user. Our methods can be regarded as generalizations of some classical closed-loop identification approaches for the linear time-invariant case. We provide an asymptotic analysis of the methods, and demonstrate their properties in a simulation example.

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  • 2.
    Abdalmoaty, Mohamed
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Learning Stochastic Nonlinear Dynamical Systems Using Non-stationary Linear Predictors2017Licentiate thesis, monograph (Other academic)
    Abstract [en]

    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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  • 3.
    Abdalmoaty, Mohamed R.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem⁎2018In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 784-789Article in journal (Refereed)
    Abstract [en]

    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.

  • 4.
    Abdalmoaty, Mohamed R.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Identification of a Class of Nonlinear Dynamical Networks⁎2018In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 868-873Article in journal (Refereed)
    Abstract [en]

    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.

  • 5.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Eriksson, Oscar
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Software and Computer systems, SCS.
    Bereza-Jarocinski, Robert
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Broman, David
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Software and Computer systems, SCS.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Identification of Non-Linear Differential-Algebraic Equation Models with Process Disturbances2021In: Proceedings The 60th IEEE conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE) , 2021Conference paper (Refereed)
    Abstract [en]

    Differential-algebraic equations (DAEs) arise naturally as a result of equation-based object-oriented modeling. In many cases, these models contain unknown parameters that have to be estimated using experimental data. However, often the system is subject to unknown disturbances which, if not taken into account in the estimation, can severely affect the model's accuracy. For non-linear state-space models, particle filter methods have been developed to tackle this issue. Unfortunately, applying such methods to non-linear DAEs requires a transformation into a state-space form, which is particularly difficult to obtain for models with process disturbances. In this paper, we propose a simulation-based prediction error method that can be used for non-linear DAEs where disturbances are modeled as continuous-time stochastic processes. To the authors' best knowledge, there are no general methods successfully dealing with parameter estimation for this type of model. One of the challenges in particle filtering  methods are random variations in the minimized cost function due to the nature of the algorithm. In our approach, a similar phenomenon occurs and we explicitly consider how to sample the underlying continuous process to mitigate this problem. The method is illustrated numerically on a pendulum example. The results suggest that the method is able to deliver consistent estimates.

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  • 6.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Henrion, D.
    Rodrigues, L.
    Measures and LMIs for optimal control of piecewise-affine systems2013In: 2013 European Control Conference, ECC 2013, IEEE, 2013, p. 3173-3178, article id 6669627Conference paper (Refereed)
    Abstract [en]

    This paper considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector field, polynomial Lagrangian and semialgebraic input and state constraints. The OCP is first relaxed as an infinite-dimensional linear program (LP) over a space of occupation measures. This LP is then approached by an asymptotically converging hierarchy of linear matrix inequality (LMI) relaxations. The relaxed dual of the original LP returns a polynomial approximation of the value function that solves the Hamilton-Jacobi-Bellman (HJB) equation of the OCP. Based on this polynomial approximation, a suboptimal policy is developed to construct a state feedback in a sample-and-hold manner. The results show that the suboptimal policy succeeds in providing a suboptimal state feedback law that drives the system relatively close to the optimal trajectories and respects the given constraints.

  • 7.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Simulated Maximum Likelihood Method for Estimation of Stochastic Wiener Systems2016In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 3060-3065, article id 7798727Conference paper (Refereed)
    Abstract [en]

    This paper introduces a simulation-based method for maximum likelihood estimation of stochastic Wienersystems. It is well known that the likelihood function ofthe observed outputs for the general class of stochasticWiener systems is analytically intractable. However, when the distributions of the process disturbance and the measurement noise are available, the likelihood can be approximated byrunning a Monte-Carlo simulation on the model. We suggest the use of Laplace importance sampling techniques for the likelihood approximation. The algorithm is tested on a simple first order linear example which is excited only by the process disturbance. Further, we demonstrate the algorithm on an FIR system with cubic nonlinearity. The performance of the algorithm is compared to the maximum likelihood method and other recent techniques.

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  • 8.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem2018In: 18th IFAC Symposium on System Identification, 2018Conference paper (Refereed)
    Abstract [en]

    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 presentedand discussed.

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    0028.pdf
  • 9.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Consistent Estimators of Stochastic MIMO Wiener Models based on Suboptimal Predictors2018Conference paper (Refereed)
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  • 10.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Identification of Stochastic Nonlinear Models Using Optimal Estimating Functions2020In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 119, article id 109055Article in journal (Refereed)
    Abstract [en]

    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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  • 11.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Linear Prediction Error Methods for Stochastic Nonlinear Models2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 105, p. 49-63Article in journal (Refereed)
    Abstract [en]

    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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  • 12.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    On Re-Weighting, Regularization Selection, and Transient in Nuclear Norm Based Identification2015Conference paper (Refereed)
    Abstract [en]

    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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  • 13.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Simulated Pseudo Maximum Likelihood Identification of Nonlinear Models2017In: The 20th IFAC World Congress, Elsevier, 2017, Vol. 50, p. 14058-14063Conference paper (Refereed)
    Abstract [en]

    Nonlinear stochastic parametric models are widely used in various fields. However, for these models, the problem of maximum likelihood identification is very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the analytically intractable likelihood function and compute either the maximum likelihood or a Bayesian estimator. These methods, albeit asymptotically optimal, are computationally expensive. In this contribution, we present a simulation-based pseudo likelihood estimator for nonlinear stochastic models. It relies only on the first two moments of the model, which are easy to approximate using Monte-Carlo simulations on the model. The resulting estimator is consistent and asymptotically normal. We show that the pseudo maximum likelihood estimator, based on a multivariate normal family, solves a prediction error minimization problem using a parameterized norm and an implicit linear predictor. In the light of this interpretation, we compare with the predictor defined by an ensemble Kalman filter. Although not identical, simulations indicate a close relationship. The performance of the simulated pseudo maximum likelihood method is illustrated in three examples. They include a challenging state-space model of dimension 100 with one output and 2 unknown parameters, as well as an application-motivated model with 5 states, 2 outputs and 5 unknown parameters.

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  • 14.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Wahlberg, Bo
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    The Gaussian MLE versus the Optimally weighted LSE2020In: IEEE signal processing magazine (Print), ISSN 1053-5888, E-ISSN 1558-0792, Vol. 37, no 6, p. 195-199Article in journal (Refereed)
    Abstract [en]

    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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  • 15.
    Abdalmoaty, Mohamed
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Identication of a Class of Nonlinear Dynamical Networks2018Conference paper (Refereed)
    Abstract [en]

    Identifcation 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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  • 16.
    Rasheed-Hilmy Abdalmoaty, Mohamed
    Luleå University of Technology.
    Measures and LMIs for optimal control of piecewise-affine dynamical systems: Systematic feedback synthesis in continuous-time2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The project considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector fields and polynomial data. The OCP is relaxed as an infinite-dimensional linear program (LP) over space of occupation measures. The LP is then written as a particular instance of the generalized moment problem which is then approached by an asymptotically converging hierarchy of linear matrix inequality (LMI) relaxations. The relaxed dual of the original LP gives a polynomial approximation of the value function along optimal trajectories. Based on this polynomial approximation, a novel suboptimal policy is developed to construct a state feedback in a sample-and-hold manner. The results show that the suboptimal policy succeeds in providing a stabilizing suboptimal state feedback law that drives the system relatively close to the optimal trajectories and respects the given constraints.

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  • 17.
    Rodrigues, Diogo
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Abdalmoaty, Mohamed
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Toward tractable global solutions to bayesian point estimation problems via sparse sum-of-squares relaxations2020In: Proceedings American Control Conference, ACC 2020, Institute of Electrical and Electronics Engineers (IEEE) , 2020, p. 1501-1506Conference paper (Refereed)
    Abstract [en]

    Bayesian point estimation is commonly used for system identification owing to its good properties for small sample sizes. Although this type of estimator is usually non-parametric, Bayes estimates can also be obtained for rational parametric models, which is often of interest. However, as in maximum-likelihood methods, the Bayes estimate is typically computed via local numerical optimization that requires good initialization and cannot guarantee global optimality. In this contribution, we propose a computationally tractable method that computes the Bayesian parameter estimates with posterior certification of global optimality via sum-of-squares polynomials and sparse semidefinite relaxations. It is shown that the method is applicable to certain discrete-time linear models, which takes advantage of the rational structure of these models and the sparsity in the Bayesian parameter estimation problem. The method is illustrated on a simulation model of a resonant system that is difficult to handle when the sample size is small.

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  • 18.
    Rodrigues, Diogo
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Abdalmoaty, Mohamed
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Toward Tractable Global Solutions to Maximum-Likelihood Estimation Problems via Sparse Sum-of-Squares Relaxations2019In: 2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC), Institute of Electrical and Electronics Engineers (IEEE) , 2019, p. 3184-3189Conference paper (Refereed)
    Abstract [en]

    In system identification, the maximum-likelihood method is typically used for parameter estimation owing to a number of optimal statistical properties. However, in many cases, the likelihood function is nonconvex. The solutions are usually obtained by local numerical optimization algorithms that require good initialization and cannot guarantee global optimality. This paper proposes a computationally tractable method that computes the maximum-likelihood parameter estimates with posterior certification of global optimality via the concept of sum-of-squares polynomials and sparse semidefinite relaxations. It is shown that the method can be applied to certain classes of discrete-time linear models. This is achieved by taking advantage of the rational structure of these models and the sparsity in the maximum-likelihood parameter estimation problem. The method is illustrated on a simulation model of a resonant mechanical system where standard methods struggle.

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  • 19.
    Rodrigues, Diogo
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Abdalmoaty, Mohamed
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Jacobsen, Elling W.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Chotteau, Véronique
    KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Industrial Biotechnology.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    An Integrated Approach for Modeling and Identification of Perfusion Bioreactors via Basis Flux Modes2021In: Computers and Chemical Engineering, ISSN 0098-1354, E-ISSN 1873-4375, Vol. 149, article id 107238Article in journal (Refereed)
    Abstract [en]

    This paper discusses the challenges associated with the reliable and optimal operation of perfusion bioreactors and presents methods for modeling and identification of perfusion bioreactors as well as the vision for their integration. After presenting ageneric model of perfusion bioreactors, the paper shows how to use the concept of basis flux modes to uniquely compute reaction rates. The advantage of this concept with respect to elementary flux nodes and similar concepts in metabolic flux analysis is the reduced number of flux modes that need to be modeled. In addition, a procedure to identify the model and estimate the parameters for each reaction using Monod-type kinetics is presented. It is shown that the rational structure of these kinetic models results in optimization problems that are amenable to tractable computation of globally optimal parameter estimates. The methods are illustrated via examples with simulated or experimental data.

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