| 1. |
- 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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| 2. |
- Abdalmoaty, Mohamed R. H., 1986-, et al.
(författare)
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Identification of Non-Linear Differential-Algebraic Equation Models with Process Disturbances
- 2021
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Ingår i: 2021 60th IEEE Conference on Decision and Control (CDC). - : IEEE. - 9781665436595 - 9781665436588 - 9781665436601 ; , s. 2300-2305
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Konferensbidrag (refereegranskat)abstract
- 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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| 3. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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The Gaussian MLE versus the Optimally weighted LSE
- 2020
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Ingår i: IEEE signal processing magazine (Print). - : Institute of Electrical and Electronics Engineers (IEEE). - 1053-5888 .- 1558-0792. ; 37:6, s. 195-199
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Tidskriftsartikel (refereegranskat)abstract
- 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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| 4. |
- Bereza-Jarocinski, Robert, et al.
(författare)
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Stochastic Approximation for Identification of Non-Linear Differential-Algebraic Equations with Process Disturbances
- 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. 6712-6717
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Konferensbidrag (refereegranskat)abstract
- Differential-algebraic equations, commonly used to model physical systems, are the basis for many equation-based object-oriented modeling languages. When systems described by such equations are influenced by unknown process disturbances, estimating unknown parameters from experimental data becomes difficult. This is because of problems with the existence of well-defined solutions and the computational tractability of estimators. In this paper, we propose a way to minimize a cost function-whose minimizer is a consistent estimator of the true parameters-using stochastic gradient descent. This approach scales significantly better with the number of unknown parameters than other currently available methods for the same type of problem. The performance of the method is demonstrated through a simulation study with three unknown parameters. The experiments show a significantly reduced variance of the estimator, compared to an output error method neglecting the influence of process disturbances, as well as an ability to reduce the estimation bias of parameters that the output error method particularly struggles with.
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| 5. |
- Bombois, X., et al.
(författare)
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Network topology detection via uncertainty analysis of an identified static model
- 2021
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Ingår i: IFAC PAPERSONLINE. - : Elsevier BV. - 2405-8963. ; , s. 595-600
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Konferensbidrag (refereegranskat)abstract
- In this paper, we propose a methodology to detect the topology of a dynamic network that is based on the analysis of the uncertainty of the static characteristic of the matrix of transfer functions between the external excitations and the node signals.
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| 6. |
- Bombois, Xavier, et al.
(författare)
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On the informativity of direct identification experiments in dynamical networks
- 2023
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 148, s. 110742-
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Tidskriftsartikel (refereegranskat)abstract
- Data informativity is a crucial property to ensure the consistency of the prediction error estimate. This property has thus been extensively studied in the open-loop and in the closed-loop cases, but has only been briefly touched upon in the dynamic network case. In this paper, we consider the prediction error identification of the modules in a row of a dynamic network using the full input approach. Our main contribution is to propose a number of easily verifiable data informativity conditions for this identification problem. Among these conditions, we distinguish a sufficient data informativity condition that can be verified based on the topology of the network and a necessary and sufficient data informativity condition that can be verified via a rank condition on a matrix of coefficients that are related to a full-order model structure of the network. These data informativity conditions allow to determine different situations (i.e., different excitation patterns) leading to data informativity. In order to be able to distinguish between these different situations, we also propose an optimal experiment design problem that allows to determine the excitation pattern yielding a certain pre-specified accuracy with the least excitation power.
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| 7. |
- Bombois, Xavier, et al.
(författare)
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Robust optimal identification experiment design for multisine excitation
- 2021
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 125
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Tidskriftsartikel (refereegranskat)abstract
- In least costly experiment design, the optimal spectrum of an identification experiment is determined in such a way that the cost of the experiment is minimized under some accuracy constraint on the identified parameter vector. Like all optimal experiment design problems, this optimization problem depends on the unknown true system, which is generally replaced by an initial estimate. One important consequence of this is that we can underestimate the actual cost of the experiment and that the accuracy of the identified model can be lower than desired. Here, based on an a-priori uncertainty set for the true system, we propose a convex optimization approach that allows to prevent these issues from happening. We do this when the to-be-determined spectrum is the one of a multisine signal.
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| 8. |
- Colin, Kevin, et al.
(författare)
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Gaussian process modeling of macroscopic kinetics : a better-tailored kernel for Monod-type kinetics
- 2022
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Ingår i: 10th Vienna International Conference on Mathematical Modelling MATHMOD 2022 Vienna Austria, 27–29 July 2022. - : Elsevier BV. ; , s. 397-402
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Konferensbidrag (refereegranskat)abstract
- In bioprocesses, it is important to model the kinetics of the macroscopic rates of reactions since these are required to catch the dynamical aspects of a process. In [Wang et al. 2020], a modeling method involving Gaussian processes has been developed, using a kernel especially designed for the modeling of Monod-type kinetics (activation, inhibition, double component, neutral effect). However, as will be illustrated in this paper, when the number of training data is limited or the metabolite concentration data do not have large variations (which is generally the case for real-life data), this kernel can yield inaccurate models for the kinetics. In this paper, we develop a new kernel better tailored for the modeling of Monod-type kinetics and we show that it has good modeling performances in the case of a limited number of data. The idea is to use the particular structure of Monod-type functions in the design of the kernel, i.e., we incorporate prior knowledge in the modeling.
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| 9. |
- Colin, Kevin, et al.
(författare)
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Optimal exploration strategies for finite horizon regret minimization in some adaptive control problems
- 2023
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Ingår i: 22nd IFAC World Congress Yokohama, Japan, July 9-14, 2023. - : Elsevier BV. ; , s. 2564-2569
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Konferensbidrag (refereegranskat)abstract
- In this work, we consider the problem of regret minimization in adaptive minimum variance and linear quadratic control problems. Regret minimization has been extensively studied in the literature for both types of adaptive control problems. Most of these works give results of the optimal rate of the regret in the asymptotic regime. In the minimum variance case, the optimal asymptotic rate for the regret is log(T) which can be reached without any additional external excitation. On the contrary, for most adaptive linear quadratic problems, it is necessary to add an external excitation in order to get the optimal asymptotic rate of √T. In this paper, we will actually show from a theoretical study, as well as, in simulations that when the control horizon is pre-specified a lower regret can be obtained with either no external excitation or a new exploration type termed immediate.
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| 10. |
- Colin, Kevin, et al.
(författare)
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Regret Minimization for Linear Quadratic Adaptive Controllers Using Fisher Feedback Exploration
- 2022
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Ingår i: IEEE Control Systems Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 2475-1456. ; 6, s. 2870-2875
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Tidskriftsartikel (refereegranskat)abstract
- In this letter, we study the trade-off between exploration and exploitation for linear quadratic adaptive control. This trade-off can be expressed as a function of the exploration and exploitation costs, called cumulative regret. It has been shown over the years that the optimal asymptotic rate of the cumulative regret is in many instances O(root T). In particular, this rate can be obtained by adding a white noise external excitation, with a variance decaying as O(1/root T). As the amount of excitation is pre-determined, such approaches can be viewed as open loop control of the external excitation. In this contribution, we approach the problem of designing the external excitation from a feedback perspective leveraging the well known benefits of feedback control for decreasing sensitivity to external disturbances and system-model mismatch, as compared to open loop strategies. We base the feedback on the Fisher information matrix which is a measure of the accuracy of the model. Specifically, the amplitude of the exploration signal is seen as the control input while the minimum eigenvalue of the Fisher matrix is the variable to be controlled. We call such exploration strategies Fisher Feedback Exploration (F2E). We propose one explicit F2E design, called Inverse Fisher Feedback Exploration (IF2E), and argue that this design guarantees the optimal asymptotic rate for the cumulative regret. We provide theoretical support for IF2E and in a numerical example we illustrate benefits of IF2E and compare it with the open loop approach as well as a method based on Thompson sampling.
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