Identification, Knowledge Engineering and Digital Modeling for Adaptive and Intelligent Control

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (20 October 2022) | Viewed by 23681

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Institute for Control Sciences, Russian Academy of Sciences, 117806 Moscow, Russia
Interests: identification of control systems; estimation theory; adaptive control; model predictive control; data mining; wavelet analysis; control of technological processes in industry and energy; multi-agent systems
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V.A. Trapeznikov Institute of Control Sciences, 65, Profsoyuznaya, 117997 Moscow, Russia
Interests: power systems analysis; power systems simulation; adaptive and optimal control; mechanical engineering
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Institute of Automation and Control Process FEB RAS, 5 Radio Str., 690041 Vladivostok, Russia
Interests: system identification; predictive modeling; advanced process control
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V.A. Trapeznikov Institute of Control Sciences, 65, Profsoyuznaya, 117997 Moscow, Russia
Interests: mechanism design; game theory; power systems analysis; mechanical engineering; identification problems
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Special Issue Information

Dear Colleagues,

The Special Issue aims to bring together scientists working in various branches of control theory to discuss manufacturing control problems, including: enterprise control and digital ecosystem creation, the development of identification theory and methodology, the related mathematical problems, parameter and nonparametric and structure identification and expert analysis, problems of selection and data analysis, control systems with identifier, modelling in intelligent systems, simulation procedures and software, digital identification, reinforcement learning, quantum modeling, intelligent model predictive control, predictive cognitive issues, problems of software quality for complex systems, and global network resources of support processes of modeling and control.

Prof. Dr. Natalia Bakhtadze
Prof. Dr. Igor Yadykin
Prof. Dr. Andrei Torgashov
Prof. Dr. Nikolay Korgin
Guest Editors

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Keywords

  • identification
  • intelligent model predictive control
  • enterprise control
  • digital ecosystem creating
  • reinforcement learning
  • quantum modeling

Published Papers (15 papers)

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Editorial

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3 pages, 161 KiB  
Editorial
Preface to the Special Issue on “Identification, Knowledge Engineering and Digital Modeling for Adaptive and Intelligent Control”—Special Issue Book
by Natalia Bakhtadze
Mathematics 2023, 11(8), 1906; https://0-doi-org.brum.beds.ac.uk/10.3390/math11081906 - 18 Apr 2023
Viewed by 639
Abstract
Starting our work on this Special Issue, we assumed that the research results presented here would reflect the solutions to various problems related to production management; however, the set of identified problems showed that their solutions could be useful for a wider range [...] Read more.
Starting our work on this Special Issue, we assumed that the research results presented here would reflect the solutions to various problems related to production management; however, the set of identified problems showed that their solutions could be useful for a wider range of applications [...] Full article

Research

Jump to: Editorial

16 pages, 4825 KiB  
Article
Choice of Regularization Methods in Experiment Processing: Solving Inverse Problems of Thermal Conductivity
by Alexander Sokolov and Irina Nikulina
Mathematics 2022, 10(22), 4221; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224221 - 11 Nov 2022
Cited by 1 | Viewed by 778
Abstract
This work is aimed at numerical studies of inverse problems of experiment processing (identification of unknown parameters of mathematical models from experimental data) based on the balanced identification technology. Such problems are inverse in their nature and often turn out to be ill-posed. [...] Read more.
This work is aimed at numerical studies of inverse problems of experiment processing (identification of unknown parameters of mathematical models from experimental data) based on the balanced identification technology. Such problems are inverse in their nature and often turn out to be ill-posed. To solve them, various regularization methods are used, which differ in regularizing additions and methods for choosing the values of the regularization parameters. Balanced identification technology uses the cross-validation root-mean-square error to select the values of the regularization parameters. Its minimization leads to an optimally balanced solution, and the obtained value is used as a quantitative criterion for the correspondence of the model and the regularization method to the data. The approach is illustrated by the problem of identifying the heat-conduction coefficient on temperature. A mixed one-dimensional nonlinear heat conduction problem was chosen as a model. The one-dimensional problem was chosen based on the convenience of the graphical presentation of the results. The experimental data are synthetic data obtained on the basis of a known exact solution with added random errors. In total, nine problems (some original) were considered, differing in data sets and criteria for choosing solutions. This is the first time such a comprehensive study with error analysis has been carried out. Various estimates of the modeling errors are given and show a good agreement with the characteristics of the synthetic data errors. The effectiveness of the technology is confirmed by comparing numerical solutions with exact ones. Full article
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17 pages, 1190 KiB  
Article
Identification of Quadratic Volterra Polynomials in the “Input–Output” Models of Nonlinear Systems
by Yury Voscoboynikov, Svetlana Solodusha, Evgeniia Markova, Ekaterina Antipina and Vasilisa Boeva
Mathematics 2022, 10(11), 1836; https://0-doi-org.brum.beds.ac.uk/10.3390/math10111836 - 26 May 2022
Cited by 2 | Viewed by 1211
Abstract
In this paper, we propose a new algorithm for constructing an integral model of a nonlinear dynamic system of the “input–output” type in the form of a quadratic segment of the Volterra integro-power series (polynomial). We consider nonparametric identification of models using physically [...] Read more.
In this paper, we propose a new algorithm for constructing an integral model of a nonlinear dynamic system of the “input–output” type in the form of a quadratic segment of the Volterra integro-power series (polynomial). We consider nonparametric identification of models using physically realizable piecewise linear test signals in the time domain. The advantage of the presented approach is to obtain explicit formulas for calculating the transient responses (Volterra kernels), which determine the unique solution of the Volterra integral equations of the first kind with two variable integration limits. The numerical method proposed in the paper for solving the corresponding equations includes the use of smoothing splines. An important result is that the constructed identification algorithm has a low methodological error. Full article
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14 pages, 619 KiB  
Article
Bayes Synthesis of Linear Nonstationary Stochastic Systems by Wavelet Canonical Expansions
by Igor Sinitsyn, Vladimir Sinitsyn, Eduard Korepanov and Tatyana Konashenkova
Mathematics 2022, 10(9), 1517; https://0-doi-org.brum.beds.ac.uk/10.3390/math10091517 - 02 May 2022
Cited by 3 | Viewed by 1002
Abstract
This article is devoted to analysis and optimization problems of stochastic systems based on wavelet canonical expansions. Basic new results: (i) for general Bayes criteria, a method of synthesized methodological support and a software tool for nonstationary normal (Gaussian) linear observable stochastic systems [...] Read more.
This article is devoted to analysis and optimization problems of stochastic systems based on wavelet canonical expansions. Basic new results: (i) for general Bayes criteria, a method of synthesized methodological support and a software tool for nonstationary normal (Gaussian) linear observable stochastic systems by Haar wavelet canonical expansions are presented; (ii) a method of synthesis of a linear optimal observable system for criterion of the maximal probability that a signal will not exceed a particular value in absolute magnitude is given. Applications: wavelet model building of essentially nonstationary stochastic processes and parameters calibration. Full article
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12 pages, 23920 KiB  
Article
Differential Neural Network-Based Nonparametric Identification of Eye Response to Enforced Head Motion
by Isaac Chairez, Arthur Mukhamedov, Vladislav Prud, Olga Andrianova and Viktor Chertopolokhov
Mathematics 2022, 10(6), 855; https://0-doi-org.brum.beds.ac.uk/10.3390/math10060855 - 08 Mar 2022
Cited by 3 | Viewed by 1795
Abstract
Dynamic motion simulators cannot provide the same stimulation of sensory systems as real motion. Hence, only a subset of human senses should be targeted. For simulators providing vestibular stimulus, an automatic bodily function of vestibular–ocular reflex (VOR) can objectively measure how accurate motion [...] Read more.
Dynamic motion simulators cannot provide the same stimulation of sensory systems as real motion. Hence, only a subset of human senses should be targeted. For simulators providing vestibular stimulus, an automatic bodily function of vestibular–ocular reflex (VOR) can objectively measure how accurate motion simulation is. This requires a model of ocular response to enforced accelerations, an attempt to create which is shown in this paper. The proposed model corresponds to a single-layer spiking differential neural network with its activation functions are based on the dynamic Izhikevich model of neuron dynamics. An experiment is proposed to collect training data corresponding to controlled accelerated motions that produce VOR, measured using an eye-tracking system. The effectiveness of the proposed identification is demonstrated by comparing its performance with a traditional sigmoidal identifier. The proposed model based on dynamic representations of activation functions produces a more accurate approximation of foveal motion as the estimation of mean square error confirms. Full article
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13 pages, 607 KiB  
Article
Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition
by Jan Heiland and Benjamin Unger
Mathematics 2022, 10(3), 418; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030418 - 28 Jan 2022
Cited by 3 | Viewed by 1593
Abstract
Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the [...] Read more.
Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge–Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge–Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings. Full article
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23 pages, 1786 KiB  
Article
Robust Stabilization via Super-Stable Systems Techniques
by Svetlana A. Krasnova, Yulia G. Kokunko, Victor A. Utkin and Anton V. Utkin
Mathematics 2022, 10(1), 98; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010098 - 28 Dec 2021
Cited by 1 | Viewed by 1000
Abstract
In this paper, we propose a direct method for the synthesis of robust systems operating under parametric uncertainty of the control plant model. The developed robust control procedures are based on the assumption that the structural properties of the nominal system are conservated [...] Read more.
In this paper, we propose a direct method for the synthesis of robust systems operating under parametric uncertainty of the control plant model. The developed robust control procedures are based on the assumption that the structural properties of the nominal system are conservated over the entire range of parameter changes. The invariant-to-parametric-uncertainties transformation of the initial model to a regular form makes it possible to use the concept of super-stable systems for the synthesis of a stabilizing feedback. It is essential that the synthesis of super-stable systems is carried out not on the basis of assigning eigenvalues to the matrix of the close-loop system, but in terms of its elements. The proposed approach is applicable to a wide class of linear systems with parametric uncertainties and provides a given degree of stability. Full article
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23 pages, 4639 KiB  
Article
New Identification Approach and Methods for Plasma Equilibrium Reconstruction in D-Shaped Tokamaks
by Yuri V. Mitrishkin, Pavel S. Korenev, Artem E. Konkov, Valerii I. Kruzhkov and Nicolai E. Ovsiannikov
Mathematics 2022, 10(1), 40; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010040 - 23 Dec 2021
Cited by 5 | Viewed by 2302
Abstract
The paper deals with the identification of plasma equilibrium reconstruction in D-shaped tokamaks on the base of plasma external magnetic measurements. The methods of such identification are directed to increase their speed of response when plasma discharges are relatively short, like in the [...] Read more.
The paper deals with the identification of plasma equilibrium reconstruction in D-shaped tokamaks on the base of plasma external magnetic measurements. The methods of such identification are directed to increase their speed of response when plasma discharges are relatively short, like in the spherical Globus-M2 tokamak (Ioffe Inst., St. Petersburg, Russia). The new approach is first to apply to the plasma discharges data the off-line equilibrium reconstruction algorithm based on the Picard iterations, and obtain the gaps between the plasma boundary and the first wall, and the second is to apply new identification methods to the gap values, producing plasma shape models operating in real time. The inputs for on-line robust identification algorithms are the measurements of magnetic fluxes on magnetic loops, plasma current, and currents in the poloidal field coils measured by the Rogowski loops. The novel on-line high-performance identification algorithms are designed on the base of (i) full-order observer synthesized by linear matrix inequality (LMI) methodology, (ii) static matrix obtained by the least square technique, and (iii) deep neural network. The robust observer is constructed on the base of the LPV plant models which have the novelty that the state vector contains the gaps which are estimated by the observer, using input and output signals. The results of the simulation of the identification systems on the base of experimental data of the Globus-M2 tokamak are presented. Full article
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19 pages, 409 KiB  
Article
On Spectral Decomposition of States and Gramians of Bilinear Dynamical Systems
by Alexey Iskakov and Igor Yadykin
Mathematics 2021, 9(24), 3288; https://0-doi-org.brum.beds.ac.uk/10.3390/math9243288 - 17 Dec 2021
Cited by 4 | Viewed by 1843
Abstract
The article proves that the state of a bilinear control system can be split uniquely into generalized modes corresponding to the eigenvalues of the dynamics matrix. It is also shown that the Gramians of controllability and observability of a bilinear system can be [...] Read more.
The article proves that the state of a bilinear control system can be split uniquely into generalized modes corresponding to the eigenvalues of the dynamics matrix. It is also shown that the Gramians of controllability and observability of a bilinear system can be divided into parts (sub-Gramians) that characterize the measure of these generalized modes and their interactions. Furthermore, the properties of sub-Gramians were investigated in relation to modal controllability and observability. We also propose an algorithm for computing the Gramians and sub-Gramians based on the element-wise computation of the solution matrix. Based on the proposed algorithm, a novel criterion for the existence of solutions to the generalized Lyapunov equation is proposed, which allows, in some cases, to expand the domain of guaranteed existence of a solution of bilinear equations. Examples are provided that illustrate the application and practical use of the considered spectral decompositions. Full article
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23 pages, 7251 KiB  
Article
Maximum-Likelihood-Based Adaptive and Intelligent Computing for Nonlinear System Identification
by Hasnat Bin Tariq, Naveed Ishtiaq Chaudhary, Zeshan Aslam Khan, Muhammad Asif Zahoor Raja, Khalid Mehmood Cheema and Ahmad H. Milyani
Mathematics 2021, 9(24), 3199; https://0-doi-org.brum.beds.ac.uk/10.3390/math9243199 - 11 Dec 2021
Cited by 4 | Viewed by 1752
Abstract
Most real-time systems are nonlinear in nature, and their optimization is very difficult due to inherit stiffness and complex system representation. The computational intelligent algorithms of evolutionary computing paradigm (ECP) effectively solve various complex, nonlinear optimization problems. The differential evolution algorithm (DEA) is [...] Read more.
Most real-time systems are nonlinear in nature, and their optimization is very difficult due to inherit stiffness and complex system representation. The computational intelligent algorithms of evolutionary computing paradigm (ECP) effectively solve various complex, nonlinear optimization problems. The differential evolution algorithm (DEA) is one of the most important approaches in ECP, which outperforms other standard approaches in terms of accuracy and convergence performance. In this study, a novel application of a recently proposed variant of DEA, the so-called, maximum-likelihood-based, adaptive, differential evolution algorithm (ADEA), is investigated for the identification of nonlinear Hammerstein output error (HOE) systems that are widely used to model different nonlinear processes of engineering and applied sciences. The performance of the ADEA is evaluated by taking polynomial- and sigmoidal-type nonlinearities in two case studies of HOE systems. Moreover, the robustness of the proposed scheme is examined for different noise levels. Reliability and consistent accuracy are assessed through multiple independent trials of the scheme. The convergence, accuracy, robustness and reliability of the ADEA are carefully examined for HOE identification in comparison with the standard counterpart of the DEA. The ADEA achieves the fitness values of 1.43 × 10−8 and 3.46 × 10−9 for a population size of 80 and 100, respectively, in the HOE system identification problem of case study 1 for a 0.01 nose level, while the respective fitness values in the case of DEA are 1.43 × 10−6 and 3.46 × 10−7. The ADEA is more statistically consistent but less complex when compared to the DEA due to the extra operations involved in introducing the adaptiveness during the mutation and crossover. The current study may consider the approach of effective nonlinear system identification as a step further in developing ECP-based computational intelligence. Full article
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16 pages, 643 KiB  
Article
Analysis and Prediction of Electric Power System’s Stability Based on Virtual State Estimators
by Natalia Bakhtadze and Igor Yadikin
Mathematics 2021, 9(24), 3194; https://0-doi-org.brum.beds.ac.uk/10.3390/math9243194 - 10 Dec 2021
Cited by 3 | Viewed by 1630
Abstract
The stability of bilinear systems is investigated using spectral techniques such as selective modal analysis. Predictive models of bilinear systems based on inductive knowledge extracted by big data mining techniques are applied with associative search of statistical patterns. A method and an algorithm [...] Read more.
The stability of bilinear systems is investigated using spectral techniques such as selective modal analysis. Predictive models of bilinear systems based on inductive knowledge extracted by big data mining techniques are applied with associative search of statistical patterns. A method and an algorithm for the elementwise solution of the generalized matrix Lyapunov equation are developed for discrete bilinear systems. The method is based on calculating the sequence of values of a fixed element of the solution matrix, which depends on the product of the eigenvalues of the dynamics matrix of the linear part and the elements of the nonlinearity matrixes. A sufficient condition for the convergence of all sequences is obtained, which is also a BIBO (bounded input bounded output) systems stability condition for the bilinear system. Full article
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20 pages, 305 KiB  
Article
Methods of Ensuring Invariance with Respect to External Disturbances: Overview and New Advances
by Aleksey Antipov, Svetlana Krasnova and Victor Utkin
Mathematics 2021, 9(23), 3140; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233140 - 06 Dec 2021
Cited by 11 | Viewed by 1629
Abstract
In this paper, we carry out a demonstration and comparative analysis of known methods of the synthesis of various control laws ensuring the invariance of the output (controlled) variable with respect to external disturbances under various assumptions about their type and channels of [...] Read more.
In this paper, we carry out a demonstration and comparative analysis of known methods of the synthesis of various control laws ensuring the invariance of the output (controlled) variable with respect to external disturbances under various assumptions about their type and channels of acting on the control plant. Methods of the synthesis are presented on the example of a third-order nonlinear system with single input and single output (SISO-systems), dynamic feedback synthesis is presented at a descriptive level and the focus is on procedures of static feedback synthesis. For the systems in which the matching conditions are not satisfied, it is concluded that it is expedient to introduce smooth and bounded nonlinear local feedbacks. Within the framework of the block control principle, we developed an iterative procedure of synthesis of S-shaped sigmoid feedbacks for such systems. Nonlinear local feedbacks ensure stabilization of the output variable with the given accuracy and settling time as in a system with traditionally used linear local feedbacks with high gains. However, in contrast to it, sigmoid functions do not lead to a large overshoot of state variables and control actions. Full article
15 pages, 1237 KiB  
Article
Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle
by Andrey A. Galyaev, Pavel V. Lysenko and Evgeny Y. Rubinovich
Mathematics 2021, 9(19), 2386; https://0-doi-org.brum.beds.ac.uk/10.3390/math9192386 - 25 Sep 2021
Cited by 6 | Viewed by 1443
Abstract
This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of [...] Read more.
This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of the target being detected by the search vehicle exceeds a certain threshold value. Interception was carried out by a controlled vehicle (defender) protecting the target. An analytical estimation of this detection probability is proposed. The interception problem was formulated as an optimal stochastic control problem, which was transformed to a deterministic optimization problem. As a result, the optimal control law of the defender was found, and the optimal interception time was estimated. The deterministic problem is a simplified version of the problem whose optimal solution provides a suboptimal solution to the stochastic problem. The obtained control law was compared with classic guidance methods. All the results were obtained analytically and validated with a computer simulation. Full article
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14 pages, 4706 KiB  
Article
Multi-Output Soft Sensor with a Multivariate Filter That Predicts Errors Applied to an Industrial Reactive Distillation Process
by Vladimir Klimchenko, Andrei Torgashov, Yuri A. W. Shardt and Fan Yang
Mathematics 2021, 9(16), 1947; https://0-doi-org.brum.beds.ac.uk/10.3390/math9161947 - 15 Aug 2021
Cited by 4 | Viewed by 1541
Abstract
The paper deals with the problem of developing a multi-output soft sensor for the industrial reactive distillation process of methyl tert-butyl ether production. Unlike the existing soft sensor approaches, this paper proposes using a soft sensor with filters to predict model errors, which [...] Read more.
The paper deals with the problem of developing a multi-output soft sensor for the industrial reactive distillation process of methyl tert-butyl ether production. Unlike the existing soft sensor approaches, this paper proposes using a soft sensor with filters to predict model errors, which are then taken into account as corrections in the final predictions of outputs. The decomposition of the problem of optimal estimation of time delays is proposed for each input of the soft sensor. Using the proposed approach to predict the concentrations of methyl sec-butyl ether, methanol, and the sum of dimers and trimers of isobutylene in the output product in a reactive distillation column was shown to improve the results by 32%, 67%, and 9.5%, respectively. Full article
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13 pages, 818 KiB  
Article
Models of Strategic Decision-Making under Informational Control
by Dmitry Novikov
Mathematics 2021, 9(16), 1889; https://0-doi-org.brum.beds.ac.uk/10.3390/math9161889 - 09 Aug 2021
Cited by 4 | Viewed by 1576
Abstract
A general complex model is considered for collective dynamical strategic decision-making with explicitly interconnected factors reflecting both psychic (internal state) and behavioral (external-action, result of activity) components of agents’ activity under the given environmental and control factors. This model unifies and generalizes approaches [...] Read more.
A general complex model is considered for collective dynamical strategic decision-making with explicitly interconnected factors reflecting both psychic (internal state) and behavioral (external-action, result of activity) components of agents’ activity under the given environmental and control factors. This model unifies and generalizes approaches of game theory, social psychology, theories of multi-agent systems, and control in organizational systems by simultaneous consideration of both internal and external parameters of the agents. Two special models (of informational control and informational confrontation) contain formal results on controllability and properties of equilibriums. Interpretations of a general model are conformity (threshold behavior), consensus, cognitive dissonance, and other effects with applications to production systems, multi-agent systems, crowd behavior, online social networks, and voting in small and large groups. Full article
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