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Artykuły w czasopismach na temat „Gaussian linearization”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

Chang, R. J., and G. E. Young. "Methods and Gaussian Criterion for Statistical Linearization of Stochastic Parametrically and Externally Excited Nonlinear Systems." Journal of Applied Mechanics 56, no. 1 (1989): 179–85. http://dx.doi.org/10.1115/1.3176042.

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The methods of Gaussian linearization along with a new Gaussian Criterion used in the prediction of the stationary output variances of stable nonlinear oscillators subjected to both stochastic parametric and external excitations are presented. The techniques of Gaussian linearization are first derived and the accuracy in the prediction of the stationary output variances is illustrated. The justification of using Gaussian linearization a priori is further investigated by establishing a Gaussian Criterion. The non-Gaussian effects due to system nonlinearities and/or large noise intensities in a

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2

Anh, N. D., and W. Schiehlen. "Probabilistic criterion for Gausian equivalent linearization." Vietnam Journal of Mechanics 18, no. 2 (1996): 1–6. http://dx.doi.org/10.15625/0866-7136/10092.

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Within the scope of Gaussian equivalent linearization, a new probabilistic criterion for determining the coefficients of the linearized equivalent equation is proposed to treat stationary response of non-linear systems under zero mean Gaussian ro.nd.om excitation. Application to the Duffing oscillate subjected to white noise is presented that shows significant improvement over corresponding accuracy of the classical Gaussian equivalent linearization for both weak and strong non-linear.

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3

Chang, R. J. "Non-Gaussian Linearization Method for Stochastic Parametrically and Externally Excited Nonlinear Systems." Journal of Dynamic Systems, Measurement, and Control 114, no. 1 (1992): 20–26. http://dx.doi.org/10.1115/1.2896503.

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A new practical non-Gaussian linearization method is developed for the problem of the dynamic response of a stable nonlinear system under both stochastic parametric and external excitations. The non-Gaussian linearization system is derived through a non-Gaussian density that is constructed as the weighted sum of undetermined Gaussian densities. The undetermined Gaussian parameters are then derived through solving a set of nonlinear algebraic moment relations. The method is illustrated by a Duffing-type stochastic system with/without parametric noise excited term. The accuracy in predicting the

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4

Chang, R. J., and G. E. Young. "Prediction of Stationary Response of Robot Manipulators Under Stochastic Base and External Excitations—Statistical Linearization Approach." Journal of Dynamic Systems, Measurement, and Control 111, no. 3 (1989): 426–32. http://dx.doi.org/10.1115/1.3153071.

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The Lagrangian dynamic equation and statistical linearization for an n-dimensional manipulator subjected to both stochastic base and external excitations and geometric constraints in states are derived. The effects of utilizing a truncated Gaussian density in the linearization due to the geometry constraints are justified. The non-Gaussian effects due to the stochastic base excitation are also quantified to justify the accuracy in the prediction of the stationary output variances. Two examples of robot manipulators are selected to illustrate the accuracy of predicted variances by the lineariza

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5

Thinh, N. H., N. D. Anh, and D. A. Cuong. "An equivalent linearization for the drag force in the Morison's equation using Hermite polynomial error sample function." Vietnam Journal of Mechanics 20, no. 2 (1998): 55–64. http://dx.doi.org/10.15625/0866-7136/10021.

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Within the scope Gaussian equivalent linearization (GEL), a new mean square criterion based on Hermite polynomial error sample functions for determining the coefficients of the equivalent linearization is proposed to linearize non-linear functions of the zero mean Gaussian random process. Application to the Morison's equation for wave forces is presented that shows significant improvements over the corresponding accuracy of the classical GEL.

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6

Ricciardi, Giuseppe. "A non-Gaussian stochastic linearization method." Probabilistic Engineering Mechanics 22, no. 1 (2007): 1–11. http://dx.doi.org/10.1016/j.probengmech.2006.04.001.

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7

Garcia-Fernandez, Angel F., Filip Tronarp, and Simo Sarkka. "Gaussian Process Classification Using Posterior Linearization." IEEE Signal Processing Letters 26, no. 5 (2019): 735–39. http://dx.doi.org/10.1109/lsp.2019.2906929.

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8

Socha, L. "Linearization in Analysis of Nonlinear Stochastic Systems: Recent Results—Part I: Theory." Applied Mechanics Reviews 58, no. 3 (2005): 178–205. http://dx.doi.org/10.1115/1.1896368.

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The purpose of Part 1 of this paper is to provide a review of recent results from 1991 through 2003 in the area of theoretical aspects of statistical and equivalent linearization in the analysis of structural and mechanical nonlinear stochastic dynamic systems. First, a discussion about misunderstandings appearing in the literature in derivation of linearization coefficients for mean-square linearization criterion is presented. In Secs. 3–6 new theoretical results, including new types of criteria, nonlinearities, and excitations in the context of linearization methods, are reviewed. In particu

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9

Silva-González, Francisco L., Sonia E. Ruiz, and Alejandro Rodríguez-Castellanos. "Non-Gaussian Stochastic Equivalent Linearization Method for Inelastic Nonlinear Systems with Softening Behaviour, under Seismic Ground Motions." Mathematical Problems in Engineering 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/539738.

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A non-Gaussian stochastic equivalent linearization (NSEL) method for estimating the non-Gaussian response of inelastic non-linear structural systems subjected to seismic ground motions represented as nonstationary random processes is presented. Based on a model that represents the time evolution of the joint probability density function (PDF) of the structural response, mathematical expressions of equivalent linearization coefficients are derived. The displacement and velocity are assumed jointly Gaussian and the marginal PDF of the hysteretic component of the displacement is modeled by a mixe

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10

Chang, R. J. "Cyclostationary gaussian and non-gaussian linearization on analyzing double-well nonlinear oscillators." Mechanical Systems and Signal Processing 142 (August 2020): 106726. http://dx.doi.org/10.1016/j.ymssp.2020.106726.

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11

Bak, Juseon, Xiong Liu, Kang Sun, Kelly Chance, and Jae-Hwan Kim. "Linearization of the effect of slit function changes for improving Ozone Monitoring Instrument ozone profile retrievals." Atmospheric Measurement Techniques 12, no. 7 (2019): 3777–88. http://dx.doi.org/10.5194/amt-12-3777-2019.

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Abstract. We introduce a method that accounts for errors caused by the slit function in an optimal-estimation-based spectral fitting process to improve ozone profile retrievals from the Ozone Monitoring Instrument (OMI) ultraviolet measurements (270–330 nm). Previously, a slit function was parameterized as a standard Gaussian by fitting the full width at half maximum (FWHM) of the slit function from climatological OMI solar irradiances. This cannot account for the temporal variation in slit function in irradiance, the intra-orbit changes due to thermally induced change and scene inhomogeneity,

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12

Chang, R. J., and S. J. Lin. "Statistical Linearization Model for the Response Prediction of Nonlinear Stochastic Systems Through Information Closure Method." Journal of Vibration and Acoustics 126, no. 3 (2004): 438–48. http://dx.doi.org/10.1115/1.1688762.

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A new linearization model with density response based on information closure scheme is proposed for the prediction of dynamic response of a stochastic nonlinear system. Firstly, both probability density function and maximum entropy of a nonlinear stochastic system are estimated under the available information about the moment response of the system. With the estimated entropy and property of entropy stability, a robust stability boundary of the nonlinear stochastic system is predicted. Next, for the prediction of response statistics, a statistical linearization model is constructed with the es

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13

Bernard, Pierre, and Liming Wu. "Stochastic linearization: the theory." Journal of Applied Probability 35, no. 3 (1998): 718–30. http://dx.doi.org/10.1239/jap/1032265219.

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Very little is known about the quantitative behaviour of dynamical systems with random excitation, unless the system is linear. Known techniques imply the resolution of parabolic partial differential equations (Fokker–Planck–Kolmogorov equation), which are degenerate and of high dimension and for which there is no effective known method of resolution. Therefore, users (physicists, mechanical engineers) concerned with such systems have had to design global linearization techniques, known as equivalent statistical linearization (Roberts and Spanos (1990)). So far, there has been no rigorous just

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14

Bernard, Pierre, and Liming Wu. "Stochastic linearization: the theory." Journal of Applied Probability 35, no. 03 (1998): 718–30. http://dx.doi.org/10.1017/s0021900200016363.

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Very little is known about the quantitative behaviour of dynamical systems with random excitation, unless the system is linear. Known techniques imply the resolution of parabolic partial differential equations (Fokker–Planck–Kolmogorov equation), which are degenerate and of high dimension and for which there is no effective known method of resolution. Therefore, users (physicists, mechanical engineers) concerned with such systems have had to design global linearization techniques, known as equivalent statistical linearization (Roberts and Spanos (1990)). So far, there has been no rigorous just

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15

Chang, Guobin, Tianhe Xu, and Haitao Wang. "M-estimator based robust unscented Kalman filter through statistical linearization." Transactions of the Institute of Measurement and Control 41, no. 7 (2018): 2016–25. http://dx.doi.org/10.1177/0142331218793925.

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The robust unscented Kalman filter (UKF) is revisited in this paper from a new point of view, namely the statistical linear regression (SLR) perspective of the unscented transformation (UT). When the actual distribution of the observation noise deviates from the assumed Gaussian distribution, the performance of the filter may degrade significantly owing to lacking robustness. After linearizing the nonlinear observation equation using the SLR perspective, the M-estimator is employed to replace the weighted least-squares one, resulting in the robust UKF. Besides providing new theoretical aspects

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16

Sugimoto, S., and Y. Kubo. "A Gaussian Sum Filter Based on Stochastic Equivalent Linearization." Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2010 (May 5, 2010): 87–94. http://dx.doi.org/10.5687/sss.2010.87.

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17

Crandall, Stephen H. "On using non-Gaussian distributions to perform statistical linearization." International Journal of Non-Linear Mechanics 39, no. 9 (2004): 1395–406. http://dx.doi.org/10.1016/j.ijnonlinmec.2004.02.001.

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18

Wu, Wen-Fang. "Comparison of Gaussian closure technique and equivalent linearization method." Probabilistic Engineering Mechanics 2, no. 1 (1987): 2–8. http://dx.doi.org/10.1016/0266-8920(87)90025-7.

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19

Guoyan, Wang, A. V. Fomichev, and Dy Yiran. "Research on Improved Gaussian Smoothing Filters for SLAM Application." Mekhatronika, Avtomatizatsiya, Upravlenie 20, no. 12 (2019): 756–64. http://dx.doi.org/10.17587/mau.20.756-764.

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To address the navigation issues of the planetary rover and construct a map for the unknown environment as well as the surface of the planets in our solar system, the simultaneous localization and mapping can be seen as an alternative method. In terms of the navigation with the laser sensor, the Kalman filter and its improving algorithms, such as EKF and UKF are widely used in the the process of processing information. Nevertheless, these filter algorithms suffer from low accuracy and significant computation expensive. The EKF algorithm has a linearization process, the UKF algorithm is better

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20

Hung, Luu Xuan. "Approximate analysis of some two-degree-of-freedom nonlinear random systems by an extension of Gaussian equivalent linearization." Vietnam Journal of Mechanics 23, no. 2 (2001): 95–109. http://dx.doi.org/10.15625/0866-7136/9943.

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The paper presents the analysis of some two-degree-of-freedom nonlinear systems under random excitation using Local Mean Square Error Criterion which is an extension of Gaussian Equivalent Linearization. The results obtained shows that the new technique can be very efficiently used not only for simple-degree-of-freedom systems as presented in the previous papers, but also for multi-degree-of-freedom ones. The solution accuracy obtained by the proposed technique is much more improved than that using the traditional linearization. The conclusions in the paper point up the significance of this te

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21

Anh, N. D., and W. Schiehlen. "A technique for obtaining approximate solutions in Gaussian equivalent linearization." Computer Methods in Applied Mechanics and Engineering 168, no. 1-4 (1999): 113–19. http://dx.doi.org/10.1016/s0045-7825(98)00136-4.

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22

Karapiperis, Konstantinos, Kallol Sett, M. Levent Kavvas, and Boris Jeremić. "Fokker–Planck linearization for non-Gaussian stochastic elastoplastic finite elements." Computer Methods in Applied Mechanics and Engineering 307 (August 2016): 451–69. http://dx.doi.org/10.1016/j.cma.2016.05.001.

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23

van Lier-Walqui, Marcus, Tomislava Vukicevic, and Derek J. Posselt. "Linearization of Microphysical Parameterization Uncertainty Using Multiplicative Process Perturbation Parameters." Monthly Weather Review 142, no. 1 (2014): 401–13. http://dx.doi.org/10.1175/mwr-d-13-00076.1.

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Abstract Recent studies have shown the importance of accounting for model physics uncertainty within probabilistic forecasts. Attempts have been made at quantifying this uncertainty in terms of microphysical parameters such as fall speed coefficients, moments of hydrometeor particle size distributions, and hydrometeor densities. It has been found that uncertainty in terms of these “traditional” microphysical parameters is highly non-Gaussian, calling into question the possibility of estimating and propagating this error using Gaussian statistical techniques such as ensemble Kalman methods. Her

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24

Mokhtari, Abdellah, Abdelaziz Benallegue, and Abdelkader Belaidi. "Polynomial Linear Quadratic Gaussian and Sliding Mode Observer for a Quadrotor Unmanned Aerial Vehicle." Journal of Robotics and Mechatronics 17, no. 4 (2005): 483–95. http://dx.doi.org/10.20965/jrm.2005.p0483.

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A polynomial Linear quadratic Gaussian method is used to compute a controller which is mixed with feedback linearization to control altogether a non linear Quadrotor UAV. A dual criterion involving the minimization of the error and control signal variances is analyzed. The introduction of the feedback linearization is seen to be useful to transform the MIMO system into a non interacting one. This will facilitate the computation of spectral factorization where the behavior is like SISO system. An algorithm is developed in this context. A sliding mode observer is added to feedback loop to estima

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25

Grana, Dario. "Bayesian linearized rock-physics inversion." GEOPHYSICS 81, no. 6 (2016): D625—D641. http://dx.doi.org/10.1190/geo2016-0161.1.

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The estimation of rock and fluid properties from seismic attributes is an inverse problem. Rock-physics modeling provides physical relations to link elastic and petrophysical variables. Most of these models are nonlinear; therefore, the inversion generally requires complex iterative optimization algorithms to estimate the reservoir model of petrophysical properties. We have developed a new approach based on the linearization of the rock-physics forward model using first-order Taylor series approximations. The mathematical method adopted for the inversion is the Bayesian approach previously app

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26

Umlauft, Jonas, and Sandra Hirche. "Feedback Linearization Based on Gaussian Processes With Event-Triggered Online Learning." IEEE Transactions on Automatic Control 65, no. 10 (2020): 4154–69. http://dx.doi.org/10.1109/tac.2019.2958840.

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27

Pradlwarter, Helmut J. "Non-Gaussian linearization — an efficient tool to analyse nonlinear MDOF-systems." Nuclear Engineering and Design 128, no. 2 (1991): 175–92. http://dx.doi.org/10.1016/0029-5493(91)90099-4.

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28

SOBIECHOWSKI, C., and L. SOCHA. "STATISTICAL LINEARIZATION OF THE DUFFING OSCILLATOR UNDER NON-GAUSSIAN EXTERNAL EXCITATION." Journal of Sound and Vibration 231, no. 1 (2000): 19–35. http://dx.doi.org/10.1006/jsvi.1999.2668.

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29

Baber, Thomas T., and Mohammed N. Noori. "Modeling General Hysteresis Behavior and Random Vibration Application." Journal of Vibration and Acoustics 108, no. 4 (1986): 411–20. http://dx.doi.org/10.1115/1.3269364.

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A simple constructive technique for the development of rate-type hysteresis models for general nonlinear system is presented. The technique is used to develop hysteresis models to incorporate time history-dependent postyield restorting forces, and general pinching behavior in smoothly varying deteriorating models. Applications of these models to random vibration analysis modeling via simulation and equivalent linearization techniques under Gaussian noise excitation is presented.

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30

Berisha, G. Kassahun, and Parvendra Kumar. "F-16/MATV; Optimal Position Controller Design using Robust and Discrete Linear Quadrature Gaussian [RLQG] Controller." Science & Technology Journal 8, no. 1 (2020): 70–77. http://dx.doi.org/10.22232/stj.2020.08.01.09.

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This paper presents the robust controller design for nonlinear F-16/MATV (Multi–Axis – Thrust - Vectoring) position control system. The linearization of nonlinear flight position system is guaranteed by feedback linearization using Taylor series expansion and the optimal LQG controllers are designed to achieve the steady state flight condition. The comparison of the using continuous and discrete LQG is fully discussed for control system. First the continuous optimal LQG controller is designed for continuous time state space represented flight dynamic system based on separation principle. But t

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31

Sugimoto, Sueo, Yukihiro Kubo, and Masaharu Ohashi. "Further Investigation of a Gaussian Sum Filter Based on Stochastic Equivalent Linearization." Transactions of the Institute of Systems, Control and Information Engineers 26, no. 11 (2013): 415–24. http://dx.doi.org/10.5687/iscie.26.415.

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32

Sugimoto, S., Y. Kubo, and M. Ohashi. "Further Investigation of a Gaussian Sum Filter Based on Stochastic Equivalent Linearization." Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2013 (May 5, 2013): 1–8. http://dx.doi.org/10.5687/sss.2013.1.

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33

Kimura, K., H. Yasumuro, and M. Sakata. "Non-Gaussian equivalent linearization for non-stationary random vibration of hysteretic system." Probabilistic Engineering Mechanics 9, no. 1-2 (1994): 15–22. http://dx.doi.org/10.1016/0266-8920(94)90025-6.

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34

Liu, Yong, Lu-yun Chen, and Hong Yi. "Equivalent stochastic linearization for nonlinear uncertain structure under stationary Gaussian stochastic excitation." Journal of Shanghai Jiaotong University (Science) 19, no. 1 (2014): 123–28. http://dx.doi.org/10.1007/s12204-014-1480-z.

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35

Önkol, Mert, and Coşku Kasnakoğlu. "Adaptive Model Predictive Control of a Two-wheeled Robot Manipulator with Varying Mass." Measurement and Control 51, no. 1-2 (2018): 38–56. http://dx.doi.org/10.1177/0020294018758527.

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This paper presents the adaptive model predictive control approach for a two-wheeled robot manipulator with varying mass. The mass variation corresponds to the robot picking and placing objects or loads from one place to another. A linear parameter varying model of the system is derived consisting of local linear models of the system at different values of the varying parameter. An adaptive model predictive control controller is designed to control the fast-varying center of gravity angle in the inner loop. The reference for the inner loop is generated by a slower outer loop controlling the li

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36

Orlova, I. S. "LINEARIZATION OF PFAFF DIFFERENTIAL EQUATIONS FOR THE CONDITIONAL QUANTILE OF MULTIVARIATE PROBABILITY DISTRIBUTIONS." Vestnik of Samara University. Natural Science Series 21, no. 10 (2017): 29–39. http://dx.doi.org/10.18287/2541-7525-2015-21-10-29-39.

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The article is devoted to the task of bringing the point transformations of nonlinear partial diﬀerential equations of Pfaﬀ for conditional quantile multi- variate probability distributions to the Pfaﬀ diﬀerential equations with constant coeﬃcients. Solutions of the equations of Pfaﬀ with constant coeﬃcients are linear functions representing the conditional quantile of multivariate Gaussian distributions.

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37

Awais, Muhammad, Laiq Khan, Saghir Ahmad, and Mohsin Jamil. "Feedback-Linearization-Based Fuel-Cell Adaptive-Control Paradigm in a Microgrid Using a Wavelet-Entrenched NeuroFuzzy Framework." Energies 14, no. 7 (2021): 1850. http://dx.doi.org/10.3390/en14071850.

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The article portrays an adaptive control paradigm for the swift response of a solid-oxide fuel cell (SOFC) in a grid-connected microgrid. The control scheme is based on an adaptive feedback-linearization-embedded fully recurrent NeuroFuzzy Laguerre wavelet control (FBL-FRNF-Lag-WC) framework. The nonlinear functions of feedback linearization (FBL) are estimated using a fully recurrent NeuroFuzzy Laguerre wavelet control (FRNF-Lag-WC) architecture with a recurrent Gaussian membership function in the antecedent part and a recurrent Laguerre wavelet in the consequent part, respectively. The perfo

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38

Kapoor, Mamta, and Kirti Rawal. "Radial basis function neural network for solution of two-dimensional burgers’ equation." Physica Scripta 99, no. 6 (2024): 066002. http://dx.doi.org/10.1088/1402-4896/ad3f9a.

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Abstract In present research a neural network-based method named as ‘Radial basis function neural network method’ is tested upon two-dimensional Burgers’ equation. For this purpose, five types of the radial basis functions are considered such as; Linear, Cubic, Quintic, Multiquadric, and gaussian. The validation of results is provided via L ∞ error, Mean Square Error, and the Root Mean Square Error. The obtained errors are acceptable from mathematical view point. The graphical compatibility of the results is also tested via the comparison of exact and predicted solutions in the graphs. It is a

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Hung, Luu Xuan. "Linearization of randomly excited nonlinear systems by using local mean square error criterion." Vietnam Journal of Mechanics 22, no. 2 (2000): 111–23. http://dx.doi.org/10.15625/0866-7136/9969.

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The paper presents the analysis of three non-linear systems under random excitation by using Local Mean Square Error Criterion which is an extension of Gaussian Equivalent Linearization proposed by Caughey. The obtained results shows that the new technique allows to get much more accurate solutions than .that using Caughey Criterion. The paper leads out some new conclusions which have not been found yet by the previous researches. The new conclusions more clarify the significance of this technique.

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40

Saha, Nilanjan, and D. Roy. "Higher order weak linearizations of stochastically driven nonlinear oscillators." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2083 (2007): 1827–56. http://dx.doi.org/10.1098/rspa.2007.1852.

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We present derivative-free weak and strong solutions of stochastically driven nonlinear oscillators of engineering interest using higher order forms of the locally transversal linearization (LTL) method. Unlike strong solutions, weak stochastic solutions attempt to predict only mathematical expectations of functions of the true solution and are obtainable with much less computational effort. The linearized equations corresponding to the higher order implicit LTL schemes are arrived at using backward Euler–Maruyama and Newmark expansions in order to conditionally replace nonlinear drift and mul

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41

Wang, Zhan, Alain Lambert, Yuwei Meng, Rongdong Yu, Jin Wang, and Wei Wang. "Consistency-Oriented SLAM Approach: Theoretical Proof and Numerical Validation." Electronics 14, no. 15 (2025): 2966. https://doi.org/10.3390/electronics14152966.

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Simultaneous Localization and Mapping (SLAM) has long been a fundamental and challenging task in robotics literature, where safety and reliability are the critical issues for successfully autonomous applications of robots. Classically, the SLAM problem is tackled via probabilistic or optimization methods (such as EKF-SLAM, Fast-SLAM, and Graph-SLAM). Despite their strong performance in real-world scenarios, these methods may exhibit inconsistency, which is caused by the inherent characteristic of model linearization or Gaussian noise assumption. In this paper, we propose an alternative monocul

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42

Wang, Tianjing, Lanyong Zhang, and Sheng Liu. "Improved Robust High-Degree Cubature Kalman Filter Based on Novel Cubature Formula and Maximum Correntropy Criterion with Application to Surface Target Tracking." Journal of Marine Science and Engineering 10, no. 8 (2022): 1070. http://dx.doi.org/10.3390/jmse10081070.

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Robust nonlinear filtering is an important method for tracking maneuvering targets in non-Gaussian noise environments. Although there are many robust filters for nonlinear systems, few of them have ideal performance for mixed Gaussian noise and non-Gaussian noise (such as scattering noise) in practical applications. Therefore, a novel cubature formula and maximum correntropy criterion (MCC)-based robust cubature Kalman filter is proposed. First, the fully symmetric cubature criterion and high-order divided difference are used to construct a new fifth-degree cubature formula using fewer symmetr

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43

Wang, Ziqi, and Junho Song. "Equivalent linearization method using Gaussian mixture (GM-ELM) for nonlinear random vibration analysis." Structural Safety 64 (January 2017): 9–19. http://dx.doi.org/10.1016/j.strusafe.2016.08.005.

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Jiang, Wen-An, and Li-Qun Chen. "An equivalent linearization technique for nonlinear piezoelectric energy harvesters under Gaussian white noise." Communications in Nonlinear Science and Numerical Simulation 19, no. 8 (2014): 2897–904. http://dx.doi.org/10.1016/j.cnsns.2013.12.037.

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Kimura, Koji, Masashi Komada, and Masaru Sakata. "Non-Gaussian Equivalent Linearization for Estimation of Stochastic Response Distribution of Nonlinear Systems." Transactions of the Japan Society of Mechanical Engineers Series C 61, no. 583 (1995): 831–35. http://dx.doi.org/10.1299/kikaic.61.831.

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Maiti, A., and S. Pathak. "A Modified Holling-Tanner Model in Stochastic Environment." Nonlinear Analysis: Modelling and Control 14, no. 1 (2009): 51–71. http://dx.doi.org/10.15388/na.2009.14.1.14530.

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Recently, a modified version of the so called Holling-Tannermodel isintroduced in the ecological literature. A detailed account of the deterministic dynamicsof this model is presented. The growth rates of the prey and predator are then perturbedby Gaussian white noises to take into account the effect of fluctuating environment. Theresulting stochastic model is cultured by the technique of statistical linearization andcriteria for non-equilibrium fluctuation and stability arederived. Numerical simulationsare carried out. The implications of our analytical findingsare addressed critically.

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QIAO, HUIJIE, and JINQIAO DUAN. "TOPOLOGICAL EQUIVALENCE FOR DISCONTINUOUS RANDOM DYNAMICAL SYSTEMS AND APPLICATIONS." Stochastics and Dynamics 14, no. 01 (2013): 1350007. http://dx.doi.org/10.1142/s021949371350007x.

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After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological equivalence (or conjugacy) for such an Itô stochastic differential equation and its transformed random differential equation is established. Consequently, a stochastic Hartman–Grobman theorem is proved for the linearization of the Itô stochastic differential equation. Furthermore, for Marcus stochastic differential equations, this topological e

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M. Lazim, Izzuddin, Abdul Rashid Husain, Nurul Adilla Mohd Subha, and Mohd Ariffanan Mohd Basri. "Intelligent Observer-Based Feedback Linearization for Autonomous Quadrotor Control." International Journal of Engineering & Technology 7, no. 4.35 (2018): 904. http://dx.doi.org/10.14419/ijet.v7i4.35.26280.

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The presence of disturbances can cause instability to the quadrotor flight and can be dangerous especially when operating near obstacles or other aerial vehicles. In this paper, a hybrid controller called state feedback with intelligent disturbance observer-based control (SF-iDOBC) is developed for trajectory tracking of quadrotor in the presence of time-varying disturbances, e.g. wind. This is achieved by integrating artificial intelligence (AI) technique with disturbance observer-based feedback linearization to achieve a better disturbance rejection capability. Here, the observer estimates t

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NIKOLIC, J., Z. PERIC, D. ALEKSIC, and D. ANTIC. "Linearization of Optimal Compressor Function and Design of Piecewise Linear Compandor for Gaussian Source." Advances in Electrical and Computer Engineering 13, no. 4 (2013): 73–78. http://dx.doi.org/10.4316/aece.2013.04013.

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Anh, N. D., and L. X. Hung. "An improved criterion of Gaussian equivalent linearization for analysis of non-linear stochastic systems." Journal of Sound and Vibration 268, no. 1 (2003): 177–200. http://dx.doi.org/10.1016/s0022-460x(03)00246-3.

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