| 1. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Continuous Time-Delay Estimation From Sampled Measurements
- 2023
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 56:2, s. 6982-6987
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Tidskriftsartikel (refereegranskat)abstract
- An algorithm for continuous time-delay estimation from sampled output data and a known input of finite energy is presented. The continuous time-delay modeling allows for the estimation of subsample delays. The proposed estimation algorithm consists of two steps. First, the continuous Laguerre spectrum of the output (delayed) signal is estimated from discretetime (sampled) noisy measurements. Second, an estimate of the delay value is obtained via a Laguerre domain model using a continuous-time description of the input. The second step of the algorithm is shown to be intrinsically biased, the bias sources are established, and the bias itself is modeled. The proposed delay estimation approach is compared in a Monte-Carlo simulation with state-of-the-art methods implemented in time, frequency, and Laguerre domain demonstrating comparable or higher accuracy in the considered scenario.
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| 2. |
- Abdalmoaty, Mohamed, 1986-
(författare)
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Identification of Stochastic Nonlinear Dynamical Models Using Estimating Functions
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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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| 3. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Identification of Stochastic Nonlinear Models Using Optimal Estimating Functions
- 2020
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 119
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Tidskriftsartikel (refereegranskat)abstract
- 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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| 4. |
- 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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| 5. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Linear Prediction Error Methods for Stochastic Nonlinear Models
- 2019
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 105, s. 49-63
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Tidskriftsartikel (refereegranskat)abstract
- 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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| 6. |
- Abdalmoaty, Mohamed, et al.
(författare)
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Measures and LMIs for optimal control of piecewise-affine systems
- 2013
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Ingår i: 2013 European Control Conference, ECC 2013. - : IEEE. - 9783033039629 ; , s. 3173-3178
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 7. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Noise reduction in Laguerre-domain discrete delay estimation
- 2022
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Ingår i: 2022 IEEE 61st Conference on Decision and Control (CDC). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781665467612 - 9781665467605 - 9781665467629 ; , s. 6254-6259
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Konferensbidrag (refereegranskat)abstract
- This paper introduces a stochastic framework for a recently proposed discrete-time delay estimation method in Laguerre-domain, i.e. with the delay block input and output signals being represented by the corresponding Laguerre series. A novel Laguerre-domain disturbance model allowing the involved signals to be square-summable sequences is devised. The relation to two commonly used time-domain disturbance models is clarified. Furthermore, by forming the input signal in a certain way, the signal shape of an additive output disturbance can be estimated and utilized for noise reduction. It is demonstrated that a significant improvement in the delay estimation error is achieved when the noise sequence is correlated. The noise reduction approach is applicable to other Laguerre-domain problems than pure delay estimation.
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| 8. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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On Re-Weighting, Regularization Selection, and Transient in Nuclear Norm Based Identification
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 48:28, s. 92-97
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Tidskriftsartikel (refereegranskat)abstract
- 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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| 9. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Privacy and Security in Network Controlled Systems via Dynamic Masking
- 2023
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 56:2, s. 991-996
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose a new architecture to enhance the privacy and security of networked control systems against malicious adversaries. We consider an adversary which first learns the system using system identification techniques (privacy), and then performs a data injection attack (security). In particular, we consider an adversary conducting zero-dynamics attacks (ZDA) which maximizes the performance cost of the system whilst staying undetected. Using the proposed architecture, we show that it is possible to (i) introduce significant bias in the system estimates obtained by the adversary: thus providing privacy, and (ii) efficiently detect attacks when the adversary performs a ZDA using the identified system: thus providing security. Through numerical simulations, we illustrate the efficacy of the proposed architecture
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| 10. |
- Abdalmoaty, Mohamed Rasheed, 1986-, et al.
(författare)
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A Simulated Maximum Likelihood Method for Estimation of Stochastic Wiener Systems
- 2016
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Ingår i: 2016 IEEE 55th Conference on Decision and Control (CDC). - : IEEE. - 9781509018376 - 9781509018444 - 9781509018383 ; , s. 3060-3065
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Konferensbidrag (refereegranskat)abstract
- 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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