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Journal articles on the topic 'Nonlinear adaptive models'

Author: Grafiati

Published: 6 September 2023

Last updated: 31 July 2025

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1

Shapiro, Arnold F., and R. Paul Gorman. "Implementing adaptive nonlinear models." Insurance: Mathematics and Economics 26, no. 2-3 (2000): 289–307. http://dx.doi.org/10.1016/s0167-6687(00)00036-6.

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2

Priscoli, F. Delli, L. Marconi, and A. Isidori. "Adaptive observers as nonlinear internal models." Systems & Control Letters 55, no. 8 (2006): 640–49. http://dx.doi.org/10.1016/j.sysconle.2005.09.016.

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3

Ye, Xudong. "Nonlinear adaptive control using multiple identification models." Systems & Control Letters 57, no. 7 (2008): 578–84. http://dx.doi.org/10.1016/j.sysconle.2007.12.007.

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4

Coad, D. S., and M. B. Woodroofe. "Corrected confidence intervals for adaptive nonlinear regression models." Journal of Statistical Planning and Inference 130, no. 1-2 (2005): 63–83. http://dx.doi.org/10.1016/j.jspi.2004.02.020.

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5

Annaswamy, A. M., C. Thanomsat, N. Mehta, and Ai-Poh Loh. "Applications of Adaptive Controllers to Systems With Nonlinear Parametrization." Journal of Dynamic Systems, Measurement, and Control 120, no. 4 (1998): 477–87. http://dx.doi.org/10.1115/1.2801489.

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Nonlinear parametrizations occur in dynamic models of several complex engineering problems. The theory of adaptive estimation and control has been applicable, by and large, to problems where parameters appear linearly. We have recently developed an adaptive controller that is capable of estimating parameters that appear nonlinearly in dynamic systems in a stable manner. In this paper, we present this algorithm and its applicability to two problems, temperature regulation in chemical reactors and precise positioning using magnetic bearings both of which contain nonlinear parametrizations. It is

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6

Murray-Smith, Roderick, and Daniel Sbarbaro. "NONLINEAR ADAPTIVE CONTROL USING NONPARAMETRIC GAUSSIAN PROCESS PRIOR MODELS." IFAC Proceedings Volumes 35, no. 1 (2002): 325–30. http://dx.doi.org/10.3182/20020721-6-es-1901.01040.

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7

Fink, Alexander, Martin Fischer, and Oliver Nelles. "Supervision of nonlinear adaptive controllers based on fuzzy models." IFAC Proceedings Volumes 32, no. 2 (1999): 8602–7. http://dx.doi.org/10.1016/s1474-6670(17)57467-4.

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8

Chen, Lingji, and Kumpati S. Narendra. "Nonlinear adaptive control using neural networks and multiple models." Automatica 37, no. 8 (2001): 1245–55. http://dx.doi.org/10.1016/s0005-1098(01)00072-3.

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9

McLain, Richard B., and Michael A. Henson. "Nonlinear Model Reference Adaptive Control with Embedded Linear Models." Industrial & Engineering Chemistry Research 39, no. 8 (2000): 3007–17. http://dx.doi.org/10.1021/ie990088t.

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10

Fink, Alexander, Martin Fischer, Oliver Nelles, and Rolf Isermann. "Supervision of nonlinear adaptive controllers based on fuzzy models." Control Engineering Practice 8, no. 10 (2000): 1093–105. http://dx.doi.org/10.1016/s0967-0661(00)00059-9.

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11

Ma, Zixiao, Zhaoyu Wang, Yifei Guo, Yuxuan Yuan, and Hao Chen. "Nonlinear Multiple Models Adaptive Secondary Voltage Control of Microgrids." IEEE Transactions on Smart Grid 12, no. 1 (2021): 227–38. http://dx.doi.org/10.1109/tsg.2020.3023307.

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12

Moussas, Vassilios C., Sokratis K. Katsikas, and Demetrios G. Lainiotis. "Adaptive Estimation of FCG Using Nonlinear State-Space Models." Stochastic Analysis and Applications 23, no. 4 (2005): 705–22. http://dx.doi.org/10.1081/sap-200064462.

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13

Lyu, Hongli, Yanan Lyu, Yongchao Gao, Heng Qian, and Shan Du. "MIMO fuzzy adaptive control systems based on fuzzy semi-tensor product." Mathematical Modelling and Control 3, no. 4 (2023): 316–30. http://dx.doi.org/10.3934/mmc.2023026.

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<abstract><p>Based on fuzzy semi-tensor product (STP) algorithms and fuzzy relation matrix (FRM) models, the design of an adaptive fuzzy controller was proposed in this paper for the multivariable nonlinear systems with uncertainty. The controlled multi-input-and-multi-output (MIMO) plants were expressed and processed first by FRM models and fuzzy STP operations, and then the indirect adaptive fuzzy control laws were designed. The tracking property of the FRM models was proved for the control objective of MIMO systems. The effectiveness of the novel matrix expression was verified b

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14

Ke, Haisen, and Jiang Li. "Adaptive Control for a Class of Nonlinear System with Redistributed Models." Journal of Control Science and Engineering 2012 (2012): 1–6. http://dx.doi.org/10.1155/2012/409139.

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Multiple model adaptive control has been investigated extensively during the last ten years in which the “switching” or “switching and tuning” have emerged as the mainly approaches. It is the “switching” that can improve the transient performance to some extent and also make it difficult to analyze the stability of the system with multiple models adaptive controller. Towards this goal, this paper develops a novel multiple models adaptive controller for a class of nonlinear system in parameter-strict-feedback form which not only improves the transient performance significantly, but also guarant

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15

Befigiannis, G. N., E. N. Demiris, and S. D. Likothanassis. "Evolutionary Nonlinear Multimodel Partitioning Filters." Journal of Advanced Computational Intelligence and Intelligent Informatics 5, no. 1 (2001): 8–14. http://dx.doi.org/10.20965/jaciii.2001.p0008.

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The problem of designing adaptive filters for nonlinear systems is faced in this work. The proposed evolution program combines the effectiveness of multimodel adaptive filters and the robustness of genetic algorithms (GAs). Specifically, a bank of different extended Kalman filters is implemented. Then, the a posteriori probability that a specific model of the bank of conditional models is the true one can be used as a GA fitness function. The superiority of the algorithm is that it evolves concurrently the models’ population with initial conditions. Thus, this procedure alleviates extended Kal

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16

PAVKOVIĆ, Danijel, Sandra STANKOVIĆ, Karlo KVATERNIK, Nikolina SITAR, and Mihael CIPEK. "Adaptive Models for Improved Battery Charging Systems / Adaptivni modeli za poboljšane sisteme punjenja baterija." Energija, ekonomija, ekologija XXVI, no. 2 (2024): 1–9. http://dx.doi.org/10.46793/eee24-2.01p.

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During its operation, sometimes it is a needed to swiftly replenish the battery from a partially depleted state, while strictly adhering to its technological limitations such as the battery terminal voltage and rated continuous charging current. To achieve this goal, this contribution outlines the dynamic battery recharging system, utilizing feedback provided by the nonlinear estimator of the battery state-of-charge (SoC) or SoC-related open-circuit-voltage (OCV). In the former case, the estimator is realized as an extended Kalman filter (EKF), while in the latter case it is implemented using

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17

Chikkula, Yugender, and Jay H. Lee. "Robust Adaptive Predictive Control of Nonlinear Processes Using Nonlinear Moving Average System Models." Industrial & Engineering Chemistry Research 39, no. 6 (2000): 2010–23. http://dx.doi.org/10.1021/ie990393e.

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18

Bando, Mai, and Akira Ichikawa. "Adaptive Regulation of Nonlinear Systems by Output Feedback." Journal of Robotics and Mechatronics 20, no. 5 (2008): 719–25. http://dx.doi.org/10.20965/jrm.2008.p0719.

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In this paper adaptive regulation by output feedback is considered for a class of single-input/single-output nonlinear systems described by multiple linear models. The adaptive laws are based on the filtered state and input of an adaptive observer. Then a controller is given by a state-dependent Riccati equation, which assures the stability of the adaptive system. Simulation results are given to illustrate the theory.

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19

El Hamidi, Khadija, Mostafa Mjahed, Abdeljalil El Kari, and Hassan Ayad. "Adaptive Control Using Neural Networks and Approximate Models for Nonlinear Dynamic Systems." Modelling and Simulation in Engineering 2020 (August 26, 2020): 1–13. http://dx.doi.org/10.1155/2020/8642915.

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In this research, a comparative study of two recurrent neural networks, nonlinear autoregressive with exogenous input (NARX) neural network and nonlinear autoregressive moving average (NARMA-L2), and a feedforward neural network (FFNN) is performed for their ability to provide adaptive control of nonlinear systems. Three dynamical nonlinear systems of different complexity are considered. The aim of this work is to make the output of the plant follow the desired reference trajectory. The problem becomes more challenging when the dynamics of the plants are assumed to be unknown, and to tackle th

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20

Satpathy, Anurag, Ganapati Panda, Rajasekhar Gogula, and Renu Sharma. "Low Complexity Adaptive Nonlinear Models for the Diagnosis of Periodontal Disease." International Journal of Sensors, Wireless Communications and Control 10, no. 4 (2020): 508–21. http://dx.doi.org/10.2174/2210327909666191211125358.

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Background / Objective: The paper addresses a specific clinical problem of diagnosis of periodontal disease with an objective to develop and evaluate the performance of low complexity Adaptive Nonlinear Models (ANM) using nonlinear expansion schemes and describes the basic structure and development of ANMs in detail. Methods: Diagnostic data pertaining to periodontal findings of teeth obtained from patients have been used as inputs to train and validate the proposed models. Results: Results obtained from simulations experiments carried out using various nonlinear expansion schemes have been co

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21

Branch, William A., Troy Davig, and Bruce McGough. "ADAPTIVE LEARNING IN REGIME-SWITCHING MODELS." Macroeconomic Dynamics 17, no. 5 (2012): 998–1022. http://dx.doi.org/10.1017/s1365100511000800.

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We study adaptive learning in economic environments subject to recurring structural change. Stochastically evolving institutional and policymaking features can be described by regime-switching models with parameters that evolve according to finite state Markov processes. We demonstrate that in nonlinear models of this form, the presence of sunspot equilibria implies two natural schemes for learning the conditional means of endogenous variables: under mean value learning, agents condition on a sunspot variable that captures the self-fulfilling serial correlation in the equilibrium, whereas unde

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22

Kürten, Karl E. "Adaptive architectures for Hebbian network models." Journal de Physique I 2, no. 5 (1992): 615–24. http://dx.doi.org/10.1051/jp1:1992105.

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23

Freise, Fritjof, Norbert Gaffke, and Rainer Schwabe. "Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models." Metrika 84, no. 6 (2021): 851–74. http://dx.doi.org/10.1007/s00184-020-00803-0.

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AbstractThe paper continues the authors’ work (Freise et al. The adaptive Wynn-algorithm in generalized linear models with univariate response. arXiv:1907.02708, 2019) on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper the asymptotics of adaptive least squares estimators under the adaptive Wynn algorithm is studied. Strong consistency and asymptotic normality are derived for two classes of nonlinear models: firstly, for the class of models satisfying a condition of ‘saturated identifiability’, which was introduced by Pronzato (Metrika 71:219–238, 2010); second

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24

Heid, Pascal, and Thomas P. Wihler. "A modified Kačanov iteration scheme with application to quasilinear diffusion models." ESAIM: Mathematical Modelling and Numerical Analysis 56, no. 2 (2022): 433–50. http://dx.doi.org/10.1051/m2an/2022008.

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The classical Kačanov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation, we introduce a modified Kačanov method, which allows for (adaptive) damping, and, thereby, to derive a new convergence analysis under more general assumptions and for a wider range of applications. For instance, in the specific context of quasilinear diffusion models, our new approach does no longer require a standard monotonicity condition on the nonlinear dif

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25

Phillips, R. F. "Partially adaptive estimation of nonlinear models via a normal mixture." Econometric Reviews 18, no. 2 (1999): 141–67. http://dx.doi.org/10.1080/07474939908800437.

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26

Roop, John Paul. "Numerical comparison of nonlinear subgridscale models via adaptive mesh refinement." Mathematical and Computer Modelling 46, no. 11-12 (2007): 1487–506. http://dx.doi.org/10.1016/j.mcm.2006.02.023.

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27

Shapiro, Arnold F. "A Hitchhiker’s guide to the techniques of adaptive nonlinear models." Insurance: Mathematics and Economics 26, no. 2-3 (2000): 119–32. http://dx.doi.org/10.1016/s0167-6687(99)00058-x.

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28

Sofianos, Nikolaos A., and Yiannis S. Boutalis. "Robust adaptive multiple models based fuzzy control of nonlinear systems." Neurocomputing 173 (January 2016): 1733–42. http://dx.doi.org/10.1016/j.neucom.2015.09.047.

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29

Li, Xiao-Li, Chao Jia, De-Xin Liu, and Da-Wei Ding. "Nonlinear adaptive control using multiple models and dynamic neural networks." Neurocomputing 136 (July 2014): 190–200. http://dx.doi.org/10.1016/j.neucom.2014.01.013.

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30

Slotine, J. J. E., and Β. E. Ydstie. "Nonlinear Process Control: An Adaptive Approach which Uses Physical Models." IFAC Proceedings Volumes 22, no. 3 (1989): 357–62. http://dx.doi.org/10.1016/s1474-6670(17)53661-7.

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31

He, Wanli, Philip Avery, and Charbel Farhat. "In situ adaptive reduction of nonlinear multiscale structural dynamics models." International Journal for Numerical Methods in Engineering 121, no. 22 (2020): 4971–88. http://dx.doi.org/10.1002/nme.6505.

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32

Fu, Yue, and Tianyou Chai. "Nonlinear multivariable adaptive control using multiple models and neural networks." Automatica 43, no. 6 (2007): 1101–10. http://dx.doi.org/10.1016/j.automatica.2006.12.010.

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33

Zhou, Jun, Zhenzhen Ge, and Jianguo Guo. "A Novel Adaptive Control Method Based on Continuous Characteristic Models." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 4 (2018): 603–10. http://dx.doi.org/10.1051/jnwpu/20183640603.

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For a class of nonlinear systems, a novel adaptive control scheme is proposed in this paper. Firstly, the continuous characteristic model is constructed, which is equivalent to its original system in output for the same input at any time. Thus, the original system can be replaced with its characteristic model for designing controllers. As the original nonlinear system has unknown parameters and unmodeled dynamics, the characteristic parameters are also unknown and fast time-varying. A novel adaptive control method is proposed by combining the continuous characteristic model with the adaptive d

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34

Prawin, J., and A. Rama Mohan Rao. "Nonlinear Structural Damage Detection Based on Adaptive Volterra Filter Model." International Journal of Structural Stability and Dynamics 18, no. 02 (2018): 1871003. http://dx.doi.org/10.1142/s0219455418710037.

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The majority of the existing damage diagnostic techniques are based on linear models. Changes in the state of the dynamics of these models, before and after damage in the structure based on the vibration measurements, are popularly used as damage indicators. However, the system may initially behave linearly and subsequently exhibit nonlinearity due to the incipience of damage. Breathing cracks that exhibit bilinear behavior are one such example of the damage induced due to nonlinearity. Further many real world structures even in their undamaged state are nonlinear. Hence, in this paper, we pre

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35

Zong, Xiao Ping, Miao Zhang, and Pei Guang Wang. "Adaptive Controller Design for SISO Switched Nonlinear Systems with Linear Uncertain Parameters." Applied Mechanics and Materials 602-605 (August 2014): 1362–66. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.1362.

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This paper presents that single input single output (SISO) switched nonlinear system tracks the variation of the state error to approach the excepted values by using model reference adaptive control (MRAC) method. In order to improve the adaptive control for nonlinear systems by Using Narendra method and dividing the system into two parts: linear and nonlinear parts. The controllers are designed to guarantee that the systems are closed to the model reference system with the arbitrary switching signal. Switching systems can ensure choose the best controller so that can enhance the performance.

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36

Comte, F., J. Dedecker, and M. L. Taupin. "ADAPTIVE DENSITY ESTIMATION FOR GENERAL ARCH MODELS." Econometric Theory 24, no. 6 (2008): 1628–62. http://dx.doi.org/10.1017/s026646660808064x.

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We consider a model Yt = σtηt in which (σt) is not independent of the noise process (ηt) but σt is independent of ηt for each t. We assume that (σt) is stationary, and we propose an adaptive estimator of the density of ln(σt2) based on the observations Yt. Under a new dependence structure, the τ-dependency defined by Dedecker and Prieur (2005, Probability Theory and Related Fields 132, 203–236), we prove that the rates of this nonparametric estimator coincide with the rates obtained in the independent and identically distributed (i.i.d.) case when (σt) and (ηt) are independent. The results app

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37

Li, Xiao-Li, De-Xin Liu, Jiang-Yun Li, and Da-Wei Ding. "Robust Adaptive Control for Nonlinear Discrete-Time Systems by Using Multiple Models." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/679039.

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Back propagation (BP) neural network is used to approximate the dynamic character of nonlinear discrete-time system. Considering the unmodeling dynamics of the system, the weights of neural network are updated by using a dead-zone algorithm and a robust adaptive controller based on the BP neural network is proposed. For the situation that jumping change parameters exist, multiple neural networks with multiple weights are built to cover the uncertainty of parameters, and multiple controllers based on these models are set up. At every sample time, a performance index function based on the identi

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38

Tie, Yu Jia, Wei Yang, and Hao Yu Tan. "Spacecraft Attitude and Orbit Coupled Nonlinear Adaptive Synchronization Control." Advanced Materials Research 327 (September 2011): 6–11. http://dx.doi.org/10.4028/www.scientific.net/amr.327.6.

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Precise dynamic model of spacecraft is essential for the space missions, to be completed successfully. Nevertheless, the independent orbit or attitude dynamic models can not meet high precision tasks. This paper developed a 6-DOF relative coupling dynamic model based upon the nonlinear relative motion dynamics equations and attitude kinematics equations described by MRP. Nonlinear synchronization control law was designed for the coupled nonlinear dynamic model, whose close-loop system was proved to be global asymptotic stable by Lyapunov direct method. Finallly, the simulation results illustra

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39

Bi, Wenjie, Yinghui Sun, Haiying Liu, and Xiaohong Chen. "Dynamic Nonlinear Pricing Model Based on Adaptive and Sophisticated Learning." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/791656.

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Existing dynamic pricing models which take consumers’ learning behavior into account generally assume that consumers learn on the basis of reinforcement learning and belief-based learning. Nevertheless, abundant empirical evidence of behavior game indicates that consumers’ learning is normally described as a process of mixed learning. Particularly, for experience goods, a consumer’s purchase decision is not only based on his previous purchase behavior (adaptive learning), but also affected by that of other consumers (sophisticated learning). With the assumption that consumers are both adaptive

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40

Bando, Mai, and Akira Ichikawa. "ADAPTIVE OUTPUT REGULATION OF NONLINEAR SYSTEMS DESCRIBED BY MULTIPLE LINEAR MODELS." IFAC Proceedings Volumes 40, no. 13 (2007): 269–74. http://dx.doi.org/10.3182/20070829-3-ru-4911.00044.

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41

Yusheng Liu and Xing-Yuan Li. "Robust adaptive control of nonlinear systems represented by input~output models." IEEE Transactions on Automatic Control 48, no. 6 (2003): 1041–45. http://dx.doi.org/10.1109/tac.2003.812797.

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42

Abed-Elhameed, Tarek M., Gamal M. Mahmoud, Motaz M. Elbadry, and Mansour E. Ahmed. "Nonlinear distributed-order models: Adaptive synchronization, image encryption and circuit implementation." Chaos, Solitons & Fractals 175 (October 2023): 114039. http://dx.doi.org/10.1016/j.chaos.2023.114039.

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43

Dukkipati, Rao V., and Satya S. Vallurupalli. "ADAPTIVE CONTROL OF AN ACTIVE SUSPENSION FOR NONLINEAR TIME VARYING VEHICLE PLANT." Transactions of the Canadian Society for Mechanical Engineering 24, no. 3-4 (2000): 525–46. http://dx.doi.org/10.1139/tcsme-2000-0039.

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This paper presents a new adaptive control approach to general multi-degrees-of-freedom suspension models. The control concept diverts from the widely applied optimal control to adaptive control. The basic idea involves obtaining optimal performance of any nonlinear time varying suspension model by adaptively following a predefined reference model. Optimal performance is achieved by an adaptive control law, which involves feed forward, feedback and auxiliary controller parameters. Model reference adaptive control is used to derive adaptation laws for the controller. The proposed control scheme

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44

Rehman, Khawar, Yung-Chieh Wang, Muhammad Waseem, and Seung Ho Hong. "Tree-based machine learning models for prediction of bed elevation around bridge piers." Physics of Fluids 34, no. 8 (2022): 085105. http://dx.doi.org/10.1063/5.0098394.

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Scouring around bridge piers is a highly nonlinear process making its prediction by deterministic and stochastic models challenging. This study explores the application of inferential models for predictions of bed elevations around bridge piers. The objective is to get a generalized machine learning model with an interpretable structure. The historical data comprise a detailed record of streamflow and bed elevations that were captured by sensors installed at the 5th Street Bridge piers over Ocmulgee River at Macon, GA. We investigate the accuracy and efficiency of various tree-based machine le

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45

Liu, Ning, Yu Sheng Liu, and Qiang Yang. "Robust Adaptive Control of Nonlinear Systems with Uncertainties." Applied Mechanics and Materials 568-570 (June 2014): 1108–12. http://dx.doi.org/10.4028/www.scientific.net/amm.568-570.1108.

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This paper proposes a robust adaptive robust controller for nonlinear systems represented by input-output models with unmodeled dynamics. Under the circumstances that the output of the system is bounded, the proposed controller can guarantee that all the variables of the system are bounded in the presence of unmodeled dynamics and time-varying disturbances. The scheme does not need to generate an additional dynamic signal to dominate the effects of the unmodeled dynamics. It is shown that the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriat

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46

Köse, Ercan, and Aydın Mühürcü. "Comparative Controlling of the Lorenz Chaotic System Using the SMC and APP Methods." Mathematical Problems in Engineering 2018 (December 6, 2018): 1–9. http://dx.doi.org/10.1155/2018/9612749.

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The Lorenz chaotic system is based on a nonlinear behavior and this causes the system to be unstable. Therefore, two different controller models were developed and named as the adaptive pole placement and sliding mode control (SMC) methods for the establishment of continuous time nonlinear Lorenz chaotic system. In order to achieve this, an improved controller structure was developed first theoretically for both the controller methods and then tested practically using the numerical samples. During the establishment of adaptive pole placement method for the Lorenz chaotic system, various stages

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47

Costa, Antonio C., Tosif Ahamed, and Greg J. Stephens. "Adaptive, locally linear models of complex dynamics." Proceedings of the National Academy of Sciences 116, no. 5 (2019): 1501–10. http://dx.doi.org/10.1073/pnas.1813476116.

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The dynamics of complex systems generally include high-dimensional, nonstationary, and nonlinear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties, we detail an approach based on local linear models within windows determined adaptively from data. While the dynamics within each window are simple, consisting of exponential decay, growth, and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a likelihood-ba

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48

Zhang, Bi, Zhizhong Mao, and Tingfeng Zhang. "Intelligent control for Hammerstein nonlinear systems with arbitrary deadzone input." Transactions of the Institute of Measurement and Control 39, no. 4 (2015): 567–78. http://dx.doi.org/10.1177/0142331215611934.

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In this paper, a new intelligent control scheme based on multiple models and neural networks is proposed to adaptively control a class of Hammerstein nonlinear systems with arbitrary deadzone input. This approach consists of a linear robust adaptive controller, multiple neural networks-based nonlinear adaptive controllers and a switching mechanism. Since the control input is derived from a modified certainty equivalent principle, the manner in which the closed-loop stability is established forms the main contribution. To show the usefulness of the developed results, three simulation examples,

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49

Siek, M., and D. P. Solomatine. "Nonlinear chaotic model for predicting storm surges." Nonlinear Processes in Geophysics 17, no. 5 (2010): 405–20. http://dx.doi.org/10.5194/npg-17-405-2010.

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Abstract. This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea,

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50

DiMattina, Christopher, and Kechen Zhang. "Active Data Collection for Efficient Estimation and Comparison of Nonlinear Neural Models." Neural Computation 23, no. 9 (2011): 2242–88. http://dx.doi.org/10.1162/neco_a_00167.

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The stimulus-response relationship of many sensory neurons is nonlinear, but fully quantifying this relationship by a complex nonlinear model may require too much data to be experimentally tractable. Here we present a theoretical study of a general two-stage computational method that may help to significantly reduce the number of stimuli needed to obtain an accurate mathematical description of nonlinear neural responses. Our method of active data collection first adaptively generates stimuli that are optimal for estimating the parameters of competing nonlinear models and then uses these estima

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