Relevant bibliographies by topics / Tangent linearization

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Academic literature on the topic 'Tangent linearization'

Author: Grafiati
Published: 5 June 2025
Last updated: 16 July 2025

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Journal articles on the topic "Tangent linearization"

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Stappers, R. J. J., and J. Barkmeijer. "Optimal linearization trajectories for tangent linear models." Quarterly Journal of the Royal Meteorological Society 138, no. 662 (2011): 170–84. http://dx.doi.org/10.1002/qj.908.

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Ngodock, H. E., S. R. Smith, and G. A. Jacobs. "Cycling the Representer Algorithm for Variational Data Assimilation with the Lorenz Attractor." Monthly Weather Review 135, no. 2 (2007): 373–86. http://dx.doi.org/10.1175/mwr3281.1.

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Abstract Realistic dynamic systems are often strongly nonlinear, particularly those for the ocean and atmosphere. Applying variational data assimilation to these systems requires a tangent linearization of the nonlinear dynamics about a background state for the cost function minimization. The tangent linearization may be accurate for limited time scales. Here it is proposed that linearized assimilation systems may be accurate if the assimilation time period is less than the tangent linear accuracy time limit. In this paper, the cycling representer method is used to test this assumption with the Lorenz attractor. The outer loops usually required to accommodate the linear assimilation for a nonlinear problem may be dropped beyond the early cycles once the solution (and forecast used as the background in the tangent linearization) is sufficiently accurate. The combination of cycling the representer method and limiting the number of outer loops significantly lowers the cost of the overall assimilation problem. In addition, this study shows that weak constraint assimilation corrects tangent linear model inaccuracies and allows extension of the limited assimilation period. Hence, the weak constraint outperforms the strong constraint method. Assimilated solution accuracy at the first cycle end is computed as a function of the initial condition error, model parameter perturbation magnitude, and outer loops. Results indicate that at least five outer loops are needed to achieve solution accuracy in the first cycle for the selected error range. In addition, this study clearly shows that one outer loop in the first cycle does not preclude accuracy convergence in future cycles.
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Ochoa-Ortega, G., R. Villafuerte-Segura, A. Luviano-Juárez, M. Ramírez-Neria, and N. Lozada-Castillo. "Cascade Delayed Controller Design for a Class of Underactuated Systems." Complexity 2020 (August 25, 2020): 1–18. http://dx.doi.org/10.1155/2020/2160743.

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In this paper, a delayed control strategy for a class of nonlinear underactuated fourth-order systems is developed. The proposal is based on the implementation of the tangent linearization technique, differential flatness, and a study of the σ-stabilization of the characteristic equation of the closed-loop system. The tangent linearization technique allows obtaining a local controllability property for the analyzed class of systems. Also, it can reduce the complexity of the global control design, through the use of a cascade connection of two second-order controllers instead of designing a global controller of the fourth-order system. The stabilizing behavior of the delayed controller design is supported by the σ-stability criterion, which provides the controller parameter selection to reach the maximum exponential decay rate on the system response. To illustrate the efficiency of the theoretical results, the proposal is experimentally assessed in two cases of study: a flexible joint system and a pendubot.
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Colajanni, P., and I. Elishakoff. "A New Look at the Stochastic Linearization Technique for Hyperbolic Tangent Oscillator." Chaos, Solitons & Fractals 9, no. 9 (1998): 1611–23. http://dx.doi.org/10.1016/s0960-0779(97)00188-4.

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Jin, Jianbing, Hai Xiang Lin, Arnold Heemink, and Arjo Segers. "Spatially varying parameter estimation for dust emissions using reduced-tangent-linearization 4DVar." Atmospheric Environment 187 (August 2018): 358–73. http://dx.doi.org/10.1016/j.atmosenv.2018.05.060.

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Messner, Mark, Armand Beaudoin, and Robert Dodds. "Consistent crystal plasticity kinematics and linearization for the implicit finite element method." Engineering Computations 32, no. 6 (2015): 1526–48. http://dx.doi.org/10.1108/ec-05-2014-0107.

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Purpose – The purpose of this paper is to describe several novel techniques for implementing a crystal plasticity (CP) material model in a large deformation, implicit finite element framework. Design/methodology/approach – Starting from the key kinematic assumptions of CP, the presentation develops the necessary CP correction terms to several common objective stress rates and the consistent linearization of the stress update algorithm. Connections to models for slip system hardening are isolated from these processes. Findings – A kinematically consistent implementation is found to require a correction to the stress update to include plastic vorticity developed by slip deformation in polycrystals. A simpler, more direct form for the algorithmic tangent is described. Several numerical examples demonstrate the capabilities and computational efficiency of the formulation. Research limitations/implications – The implementation assumes isotropic slip system hardening. With simple modifications, the described approach extends readily to anisotropic coupled or uncoupled hardening functions. Practical implications – The modular formulation and implementation support streamlined development of new models for slip system hardening without modifications of the stress update and algorithmic tangent computations. This implementation is available in the open-source code WARP3D. Originality/value – In the process of developing the CP formulation, this work realized the need for corrections to the Green-Naghdi and Jaumann objective stress rates to account properly for non-zero plastic vorticity. The paper describes fully the consistent linearization of the stress update algorithm and details a new scheme to implement the model with improved efficiency.
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Cai, Guangbin, Guangren Duan, Changhua Hu, and Bin Zhou. "Tracking control for air-breathing hypersonic cruise vehicle based on tangent linearization approach." Journal of Systems Engineering and Electronics 21, no. 3 (2010): 469–75. http://dx.doi.org/10.3969/j.issn.1004-4132.2010.03.018.

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PROTIC, Danijela, and Miomir STANKOVIC. "XOR-Based Detector of Different Decisions on Anomalies in the Computer Network Traffic." Romanian Journal of Information Science and Technology 2023, no. 3-4 (2023): 323–38. http://dx.doi.org/10.59277/romjist.2023.3-4.06.

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Anomaly-based intrusion detection systems are designed to scan computer network traffic for abnormal behavior. Binary classifiers based on supervised machine learning have proven to be highly accurate tools for classifying instances as normal or abnormal. Main disadvantages of supervised machine learning are the long processing time and large amount of training data required to ensure accurate results. Two preprocessing steps to reduce data sets are feature selection and feature scaling. In this article, we present a new hyperbolic tangent feature scaling approach based on the linearization of the tangent hyperbolic function and the damping strategy of the Levenberg-Marquardt algorithm. Experiments performed on the Kyoto 2006+ dataset used four high-precision binary classifiers: weighted k-nearest neighbors, decision tree, feedforward neural networks, and support vector machine. It is shown that hyperbolic tangent scaling reduces processing time by more than twofold. An XOR-based detector is proposed to determine conflicting decisions about anomalies. The decisions of the FNN and wk-NN models are compared. It is shown that decisions sometimes turn out differently. The percentage of the opposite decisions has been shown to vary and is not affected by dataset size.
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Aguilar-Ibanez, Carlos, Hebertt Sira-Ramirez, and Miguel S. Suarez-Castanon. "A Linear Active Disturbance Rejection Control for a Ball and Rigid Triangle System." Mathematical Problems in Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/1358930.

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This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction.
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Ramírez-Neria, Mario, Hebertt Sira-Ramírez, Rubén Garrido-Moctezuma, and Alberto Luviano-Juárez. "Active Disturbance Rejection Control of the Inertia Wheel Pendulum through a Tangent Linearization Approach." International Journal of Control, Automation and Systems 17, no. 1 (2019): 18–28. http://dx.doi.org/10.1007/s12555-017-0428-0.

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Book chapters on the topic "Tangent linearization"

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Konyukhov, Alexander, and Karl Schweizerhof. "Linearization of the Weak Forms – Tangent Matrices in a Covariant Form." In Computational Contact Mechanics. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-31531-2_7.

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Conference papers on the topic "Tangent linearization"

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Sira-Ramírez, H., E. W. Zurita-Bustamante, and E. Hernández-Flores. "On the ADRC of Non-Differentially Flat, Underactuated, Nonlinear Systems: An Experimental Case Study." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67126.

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In this article, the output reference trajectory tracking control of a non-differentially flat, underactuated, system is approached from the perspective of Active Disturbance Rejection Control (ADRC) including a suitable Extended State Observer (ESO). The class of underactuated systems, which are non-differentially flat, constitutes the most challenging area for testing the effectiveness of robust feedback control algorithms, specially under output trajectory tracking requirements. The problem, however, is substantially alleviated and feasibly approached provided the tangent linearization of the system is found to be controllable around an arbitrary equilibrium point. The flatness of the tangent system is taken advantage of for the design of an observer-based feedback controller taking the tangent system operation substantially far from the operating point. The ADRC scheme robustly takes efficient care of the excited (endogenous) nonlinearities, which were neglected in the linearization process, as well as any other external (exogenous) disturbances. Here, we take the gantry crane and its closely associated system: the inverted pendulum on a cart, as working laboratory examples to illustrate the effectiveness of the proposed approach.
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Colajanni, P., and I. Elishakoff. "A New Look at the Stochastic Linearization Technique for Hyperbolic Tangent Oscillator." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0899.

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Abstract Stochastic linearization technique is reconsidered for oscillator with restoring force in form of hyperbolic tangent. We show that a subtle error was made in the previously known procedure for derivation of the linearized system parameters. Two new error-free procedures, namely, those based on minimization of mean square difference between (a) restoring force or (b) potential energy of the original non-linear system and their linear counterparts, are suggested. The results of numerical analysis are shown.
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Kohli, Dilip, and Michael Osvatic. "Inverse Kinematics of General 6R and 5R,P Serial Manipulators." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0434.

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Abstract In this paper we present a solution to the inverse kinematics problem for serial manipulators of general geometry. The method is presented in detail as it applies to a 6R manipulator of general geometry. The equations used are derived using a linearization method and dialytic elimination. In doing this, all variables except one, a tangent half angle of a joint variable, can be eliminated. The result is a 16 by 16 matrix in which all terms are linear in the suppressed variable. The unique design of this matrix allows the suppressed variable to be solved as an eigenvalue problem. Substituting these values of the suppressed variable back into the equations, all other joint variables can be found using linear equations. The result is the 16 solutions expected for the 6R case. The same technique is also applicable to manipulators with prismatic joints. We present the solution technique for all six possible 5R,P manipulators through numerical examples. The primary distinction between the technique presented in this paper and recently published Raghavan and Roth (90a,b.c) solution is that they removed two known spurious imaginary roots of multiplicity four to obtain a 16th order polynomial for 6R and 5R,P cases. In our formulation, the 16th degree polynomial can be derived directly without having to remove any spurious imaginary roots. Another distinction is that the solution procedure presented in this paper can be reduced to an eigenvalue problem. This results in significant gains in computation time.
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Kohli, Dilip, and Michael Osvatic. "Inverse Kinematics of General 4R2P, 3R3P, 4R1C, 2R2C, and 3C Serial Manipulators." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0207.

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Abstract This paper presents a solution to the inverse kinematics problem for 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators of general geometry. The method used to solve these is based on a technique recently presented by the authors for solving the inverse kinematics of general 6R and 5R1P manipulators. In the 6R and 5R1P cases, the method initially starts using 14 linearly independent equations where as for the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulator only 3, 6, 7 or 10 linearly independent equations are required, depending on the case. Through the use of a linearization and dialytic elimination method all 4R2P, 3R3P, 4R1C, 2R2C and 3C cases are reduced to equating to zero the determinant of a matrix whose elements are linear in the tangent of a half angle of a joint variable. The size of this matrix is (8 × 8) for all 4R2P manipulators, (2 × 2) for all 3R3P and 3C manipulators, (16 × 16) for 4R1C manipulators, (4 × 4) for RCRC and CRCR manipulators and (8 × 8) for the remaining 2R2C manipulators providing 8th, 2nd, 16th, 4th and 8th degree inverse kinematic polynomial respectively. Thus, the determinant equated to zero gives us the characteristic equation of the degree expected. The unique form of the matrix allows us to obtain the solution by solving an eigenvalue problem. Many variations of the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators are presented and the solution methodology is illustrated by several numerical examples.
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