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Journal articles on the topic 'Parametric polynomial systems'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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1

Franco-Medrano, Fermin, and Francisco J. Solis. "Stability of Real Parametric Polynomial Discrete Dynamical Systems." Discrete Dynamics in Nature and Society 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/680970.

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We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameterλand generalize this characterization to cubic real polynomial maps, in a consistent theory that is further generalized to realmth degree real polynomial maps. In essence, we give conditions for the stability of the fixed points of any real polynomial map with real fixed points. In order to do this, we have introduced the concept ofcanonical polynomial mapswhich are topologically conjugate to any polynomial map of the same degree with

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2

Lazard, Daniel, and Fabrice Rouillier. "Solving parametric polynomial systems." Journal of Symbolic Computation 42, no. 6 (2007): 636–67. http://dx.doi.org/10.1016/j.jsc.2007.01.007.

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3

Lai, Yisheng, Renhong Wang, and Jinming Wu. "Solving parametric piecewise polynomial systems." Journal of Computational and Applied Mathematics 236, no. 5 (2011): 924–36. http://dx.doi.org/10.1016/j.cam.2011.05.008.

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4

Moreno Maza, Marc, Bican Xia, and Rong Xiao. "On Solving Parametric Polynomial Systems." Mathematics in Computer Science 6, no. 4 (2012): 457–73. http://dx.doi.org/10.1007/s11786-012-0136-3.

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5

Ayad, A. "Complexity of solving parametric polynomial systems." Journal of Mathematical Sciences 179, no. 6 (2011): 635–61. http://dx.doi.org/10.1007/s10958-011-0616-z.

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6

Hashemi, Amir, Benyamin M.-Alizadeh, and Mahdi Dehghani Darmian. "Minimal polynomial systems for parametric matrices." Linear and Multilinear Algebra 61, no. 2 (2012): 265–72. http://dx.doi.org/10.1080/03081087.2012.670235.

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7

Chen, Zhenghong, Xiaoxian Tang, and Bican Xia. "Generic regular decompositions for parametric polynomial systems." Journal of Systems Science and Complexity 28, no. 5 (2015): 1194–211. http://dx.doi.org/10.1007/s11424-015-3015-6.

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8

Gerhard, Jürgen, D. J. Jeffrey, and Guillaume Moroz. "A package for solving parametric polynomial systems." ACM Communications in Computer Algebra 43, no. 3/4 (2010): 61–72. http://dx.doi.org/10.1145/1823931.1823933.

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9

A.A., Nesenchuk. "Investigation and robust synthesis of polynomials under perturbations based on the root locus parameter distribution diagram." Artificial Intelligence 24, no. 1-2 (2019): 25–33. http://dx.doi.org/10.15407/jai2019.01-02.025.

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Investigation of the 4 th order dynamic systems characteristic polynomials behavior in conditions of the interval parametric uncertainties is carried out on the basis of root locus portraits. The roots behavior regularities and corresponding diagrams for the root locus parameter distribution along the asymptotic stability bound are specified for the root locus portraits of the systems. On this basis the stability conditions are derived, graphic-analytical method is worked out for calculating intervals of variation for the polynomial family parameters ensuring its robust stability. The discover

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10

HOANG, VIET HA, and CHRISTOPH SCHWAB. "REGULARITY AND GENERALIZED POLYNOMIAL CHAOS APPROXIMATION OF PARAMETRIC AND RANDOM SECOND-ORDER HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS." Analysis and Applications 10, no. 03 (2012): 295–326. http://dx.doi.org/10.1142/s0219530512500145.

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Initial boundary value problems of linear second-order hyperbolic partial differential equations whose coefficients depend on countably many random parameters are reduced to a parametric family of deterministic initial boundary value problems on an infinite dimensional parameter space. This parametric family is approximated by Galerkin projection onto finitely supported polynomial systems in the parameter space. We establish uniform stability with respect to the support of the resulting coupled hyperbolic systems, and provide sufficient smoothness and compatibility conditions on the data for t

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11

Šebek, Michael, Martin Hromčik, and Jan Ježek. "Polynomial Toolbox 2.5 and Systems with Parametric Uncertainties 1." IFAC Proceedings Volumes 33, no. 14 (2000): 757–61. http://dx.doi.org/10.1016/s1474-6670(17)36321-8.

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12

Guo, Long-Chuan. "Adaptive Output Feedback Tracking Controller Design of Stochastic Nonlinear Systems with Parameter Uncertainty for Polynomial Function Growth Conditions." Mathematical Problems in Engineering 2018 (June 19, 2018): 1–10. http://dx.doi.org/10.1155/2018/7659536.

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This paper mainly focuses on output feedback practical tracking controller design for stochastic nonlinear systems with polynomial function growth conditions. Mostly, there are some studies on output feedback tracking control problem for general nonlinear systems with parametric certainty in existing achievements. Moreover, we extend it to stochastic nonlinear systems with parametric uncertainty and system nonlinear terms are assumed to satisfy polynomial function growth conditions which are more relaxed than linear growth conditions or power growth conditions. Due to the presence of unknown p

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13

Aoki, Miho, and Yasuhiro Kishi. "On systems of fundamental units of certain quartic fields." International Journal of Number Theory 11, no. 07 (2015): 2019–35. http://dx.doi.org/10.1142/s1793042115500864.

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14

Xia, Bingqing, Hao Wu, Wenbin Yang, Lu Cao, and Yonghua Song. "Parametric Transient Stability Constrained Optimal Power Flow Solved by Polynomial Approximation Based on the Stochastic Collocation Method." Energies 15, no. 11 (2022): 4127. http://dx.doi.org/10.3390/en15114127.

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To better respond to the impact of power system-uncertain parameters on transient stability, a novel model named the parametric transient stability constrained optimal power flow (parametric TSCOPF) is proposed. It seeks the optimal control scheme of transient stability constrained optimal power flow (TSCOPF) expressed by the function of uncertain parameters in power systems. The key difficulty to solve this model lies in that the relationship between the parametric TSCOPF solution and uncertain parameters is implicit, which is hard to derive generally. To this end, this paper approximates the

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15

ZHOU, Yongzhi, Hao WU, Chenghong GU, and Yonghua SONG. "Global optimal polynomial approximation for parametric problems in power systems." Journal of Modern Power Systems and Clean Energy 7, no. 3 (2018): 500–511. http://dx.doi.org/10.1007/s40565-018-0469-2.

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16

Lewis, Robert H., Béla Paláncz, and Joseph Awange. "Solving geoinformatics parametric polynomial systems using the improved Dixon resultant." Earth Science Informatics 12, no. 2 (2018): 229–39. http://dx.doi.org/10.1007/s12145-018-0366-2.

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17

Barrowclough, Oliver J. D., and Tor Dokken. "Approximate Implicitization Using Linear Algebra." Journal of Applied Mathematics 2012 (2012): 1–25. http://dx.doi.org/10.1155/2012/293746.

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We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD) systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend

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18

Duff, Timothy, Cvetelina Hill, Anders Jensen, Kisun Lee, Anton Leykin, and Jeff Sommars. "Solving polynomial systems via homotopy continuation and monodromy." IMA Journal of Numerical Analysis 39, no. 3 (2018): 1421–46. http://dx.doi.org/10.1093/imanum/dry017.

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Abstract We study methods for finding the solution set of a generic system in a family of polynomial systems with parametric coefficients. We present a framework for describing monodromy-based solvers in terms of decorated graphs. Under the theoretical . that monodromy actions are generated uniformly, we show that the expected number of homotopy paths tracked by an algorithm following this framework is linear in the number of solutions. We demonstrate that our software implementation is competitive with the existing state-of-the-art methods implemented in other software packages.

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19

Duff, G. F. D., R. B. Leipnik, and C. E. M. Pearce. "Guide expansions for the recursive parametric solution of polynomial dynamical systems." ANZIAM Journal 47, no. 3 (2006): 387–96. http://dx.doi.org/10.1017/s1446181100009901.

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AbstractRecursive parametric series solutions are developed for polynomial ODE systems, based on expanding the system components in series of a form studied by Weiss. Individual terms involve first-order driven linear ODE systems with variable coefficients. We consider Lotka-Volterra systems as an example.

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20

Son, Jeongeun, and Yuncheng Du. "An Efficient Polynomial Chaos Expansion Method for Uncertainty Quantification in Dynamic Systems." Applied Mechanics 2, no. 3 (2021): 460–81. http://dx.doi.org/10.3390/applmech2030026.

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Uncertainty is a common feature in first-principles models that are widely used in various engineering problems. Uncertainty quantification (UQ) has become an essential procedure to improve the accuracy and reliability of model predictions. Polynomial chaos expansion (PCE) has been used as an efficient approach for UQ by approximating uncertainty with orthogonal polynomial basis functions of standard distributions (e.g., normal) chosen from the Askey scheme. However, uncertainty in practice may not be represented well by standard distributions. In this case, the convergence rate and accuracy o

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21

Solis, Francisco. "Evolution of an Exponential Polynomial Family of Discrete Dynamical Systems." Mathematical and Computational Applications 24, no. 1 (2019): 13. http://dx.doi.org/10.3390/mca24010013.

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In this paper, we introduce and analyze a family of exponential polynomial discrete dynamical systems that can be considered as functional perturbations of a linear dynamical system. The stability analysis of equilibria of this family is performed by considering three different parametric scenarios, from which we show the intricate and complex dynamical behavior of their orbits.

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22

Shen, Danfeng, Hao Wu, Bingqing Xia, and Deqiang Gan. "Polynomial Chaos Expansion for Parametric Problems in Engineering Systems: A Review." IEEE Systems Journal 14, no. 3 (2020): 4500–4514. http://dx.doi.org/10.1109/jsyst.2019.2957664.

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23

Zheng, Qian, and Fen Wu. "Adaptive control design for uncertain polynomial nonlinear systems with parametric uncertainties." International Journal of Adaptive Control and Signal Processing 25, no. 6 (2010): 502–18. http://dx.doi.org/10.1002/acs.1215.

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24

Trinchero, Riccardo, Paolo Manfredi, and Igor S. Stievano. "TMsim: An Algorithmic Tool for the Parametric and Worst-Case Simulation of Systems with Uncertainties." Mathematical Problems in Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/6739857.

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This paper presents a general purpose, algebraic tool—named TMsim—for the combined parametric and worst-case analysis of systems with bounded uncertain parameters. The tool is based on the theory of Taylor models and represents uncertain variables on a bounded domain in terms of a Taylor polynomial plus an interval remainder accounting for truncation and round-off errors. This representation is propagated from inputs to outputs by means of a suitable redefinition of the involved calculations, in both scalar and matrix form. The polynomial provides a parametric approximation of the variable, wh

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25

Ezangina, Tatiana Al, and Sergey An Gayvoronskiy. "Ensuring Maximum Stability Degree in the Systems with Interval Parameters." Applied Mechanics and Materials 752-753 (April 2015): 955–60. http://dx.doi.org/10.4028/www.scientific.net/amm.752-753.955.

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The robust control system objects with interval-undermined parameters is considers in this paper. Initial information about the system is its characteristic polynomial with interval coefficients. On the basis of coefficient estimations of quality indices and criterion of the maximum stability degree, the methods of synthesis of a robust regulator parametric is developed.

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26

Le, Huu Phuoc, and Mohab Safey El Din. "Solving parametric systems of polynomial equations over the reals through Hermite matrices." Journal of Symbolic Computation 112 (September 2022): 25–61. http://dx.doi.org/10.1016/j.jsc.2021.12.002.

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27

Ayad, Ali, Ali Fares, and Youssef Ayyad. "An algorithm for solving zero-dimensional parametric systems of polynomial homogeneous equations." Journal of Nonlinear Sciences and Applications 05, no. 06 (2012): 426–38. http://dx.doi.org/10.22436/jnsa.005.06.03.

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28

Zhou, Yongzhi, Hao Wu, Chenghong Gu, and Yonghua Song. "A Novel Method of Polynomial Approximation for Parametric Problems in Power Systems." IEEE Transactions on Power Systems 32, no. 4 (2017): 3298–307. http://dx.doi.org/10.1109/tpwrs.2016.2623820.

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29

Gavalec, Martin, and Zuzana Němcová. "Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra." Mathematics 8, no. 6 (2020): 1026. http://dx.doi.org/10.3390/math8061026.

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The max-Łukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Łukasiewicz triangular norm. The behavior of such a system in time depends on the solvability of the corresponding bounded parametric max-linear system. The aim of this study is to describe an algorithm recognizing for which values of the parameter the given bounded parametric max-linear system has a solution—represented by an appropriate state of the fuzzy system in consideration. Necessary and sufficient conditions of the solvability have been found and a

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30

LI, JIBIN, and FENGJUAN CHEN. "KNOTTED PERIODIC ORBITS AND CHAOTIC BEHAVIOR OF A CLASS OF THREE-DIMENSIONAL FLOWS." International Journal of Bifurcation and Chaos 21, no. 09 (2011): 2505–23. http://dx.doi.org/10.1142/s0218127411029896.

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This paper considers a class of three-dimensional systems constructed by rotating some planar symmetric polynomial vector fields. It shows that this class of systems has infinitely many distinct types of knotted periodic orbits, which lie on a family of invariant torus. For two three-dimensional systems, exact explicit parametric representations of the knotted periodic orbits are given. For their perturbed systems, the chaotic behavior is discussed by using two different methods.

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31

Buldaev, Alexander, and Dmitry Trunin. "On a Method for Optimizing Controlled Polynomial Systems with Constraints." Mathematics 11, no. 7 (2023): 1695. http://dx.doi.org/10.3390/math11071695.

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A new optimization approach is considered in the class of polynomial in-state optimal control problems with constraints based on nonlocal control improvement conditions, which are constructed in the form of special fixed-point problems in the control space. The proposed method of successive approximations of control retains all constraints at each iteration and does not use the operation of parametric variation of control at each iteration, in contrast to known gradient methods. In addition, the initial approximation of the iterative process may not satisfy the constraints, which is a signific

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32

Srinivasa Rao, Danaboyina, Mangipudi Siva Kumar, and Manyala Ramalinga Raju. "New algorithm for the design of robust PI controller for plants with parametric uncertainty." Transactions of the Institute of Measurement and Control 40, no. 5 (2017): 1481–89. http://dx.doi.org/10.1177/0142331216685393.

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This paper proposes a new algorithm for the design of robust PI controller for plants with parametric uncertainty using new necessary and sufficient stability conditions. Most of the control systems operate under large uncertainty causing degradation of system performance and destabilization. In order to compensate these shortcomings, a robust PI controller is designed based on new necessary and sufficient conditions for stability of a plant with parametric uncertainty, a class of interval polynomial. New necessary and sufficient conditions for the determination of robust stability of interval

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33

Gayvoronskiy, S. A., T. A. Ezangina, I. V. Khozhaev, and A. A. Nesenchuk. "Analyzing Robust Stability of an Interval Control System on the Basis of Vertex Polynomials." Mekhatronika, Avtomatizatsiya, Upravlenie 20, no. 5 (2019): 266–73. http://dx.doi.org/10.17587/mau.20.266-273.

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In the paper, a characteristic polynomial of an interval control system, whose coefficients are unknown or may vary within certain ranges of values, is considered. Parametric variations cause migration of interval characteristic polynomial roots within their allocation areas, whose borders determine robust stability degree of the interval control system. To estimate a robust stability degree, a projection of a polytope of interval characteristic polynomial coefficients on a complex plane must be examined. However, in order to find a robust stability degree it is enough to examine some vertices

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34

Wan, Yiming, Dongying Erin Shen, Sergio Lucia, Rolf Findeisen, and Richard D. Braatz. "Polynomial chaos-based H2 output-feedback control of systems with probabilistic parametric uncertainties." Automatica 131 (September 2021): 109743. http://dx.doi.org/10.1016/j.automatica.2021.109743.

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35

DU, WeiPing, YiSheng LAI, DeXin DUAN, and XiaoKe FANG. "Progress in construction of piecewise algebraic hypersurfaces and solving parametric piecewise polynomial systems." SCIENTIA SINICA Mathematica 45, no. 9 (2015): 1423–40. http://dx.doi.org/10.1360/n012015-00063.

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36

Salah, Hassan, and Mohamed Elbessa. "Using Machine Learning Techniques to Predict Significant Wave Height Compared with Parametric Methods." Engineering and Applied Sciences 9, no. 5 (2024): 106–28. http://dx.doi.org/10.11648/j.eas.20240905.12.

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Prediction of Sea Wave parameters is an important issue as it is the main design factor for maritime structures. Previously, researchers have used many parametric and numerical approaches, which may be complex in application, take a long time in preparation and sometimes require a bathymetric survey. Recently, soft computing techniques such as Fuzzy Inference Systems, Genetic Algorithm, Machine Learning, etc. have been used to predict sea wave parameters in many marine areas around the world. The ease of application, high accuracy and low computational time of these techniques make them a very

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37

Sadchikov, Pavel, Tatyana Khomenko, and Galina Ternovaya. "Numerical optimization of the transfer function of the intelligent building management system." E3S Web of Conferences 97 (2019): 01015. http://dx.doi.org/10.1051/e3sconf/20199701015.

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The paper deals with structural-parametric models for describing dynamic processes of technical systems of an intelligent building. The task of searching for the transfer function of the synthesized elements and devices of its information-measuring and control systems based on the Mason method is formalized. The components of the transfer function are presented in the form of characteristic polynomials in the structural scheme of the energy-information model of the circuit. The results of a comparative analysis of search methods for multiple real and complex conjugate polynomial roots are pres

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38

Allgower, Eugene L., and Kurt Georg. "Continuation and path following." Acta Numerica 2 (January 1993): 1–64. http://dx.doi.org/10.1017/s0962492900002336.

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The main ideas of path following by predictor–corrector and piecewise-linear methods, and their application in the direction of homotopy methods and nonlinear eigenvalue problems are reviewed. Further new applications to areas such as polynomial systems of equations, linear eigenvalue problems, interior methods for linear programming, parametric programming and complex bifurcation are surveyed. Complexity issues and available software are also discussed.

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39

Son, Jeongeun, Dongping Du, and Yuncheng Du. "Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems." Applied Mechanics 1, no. 3 (2020): 153–73. http://dx.doi.org/10.3390/applmech1030011.

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Uncertainty quantification (UQ) is an important part of mathematical modeling and simulations, which quantifies the impact of parametric uncertainty on model predictions. This paper presents an efficient approach for polynomial chaos expansion (PCE) based UQ method in biological systems. For PCE, the key step is the stochastic Galerkin (SG) projection, which yields a family of deterministic models of PCE coefficients to describe the original stochastic system. When dealing with systems that involve nonpolynomial terms and many uncertainties, the SG-based PCE is computationally prohibitive beca

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40

Sánchez, Marcelino, and Miguel Bernal. "LMI–Based Robust Control of Uncertain Nonlinear Systems via Polytopes of Polynomials." International Journal of Applied Mathematics and Computer Science 29, no. 2 (2019): 275–83. http://dx.doi.org/10.2478/amcs-2019-0020.

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Abstract This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild as

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41

COHEN, ALBERT, RONALD DEVORE, and CHRISTOPH SCHWAB. "ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S." Analysis and Applications 09, no. 01 (2011): 11–47. http://dx.doi.org/10.1142/s0219530511001728.

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Parametric partial differential equations are commonly used to model physical systems. They also arise when Wiener chaos expansions are used as an alternative to Monte Carlo when solving stochastic elliptic problems. This paper considers a model class of second order, linear, parametric, elliptic PDE's in a bounded domain D with coefficients depending on possibly countably many parameters. It shows that the dependence of the solution on the parameters in the diffusion coefficient is analytically smooth. This analyticity is then exploited to prove that under very weak assumptions on the diffusi

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42

Kopchak, Bohdan, Andrii Kushnir, Inna Onoshko, and Sergiy Vovk. "Synthesis of two-mass electromechanical systems with cascade connection of fractional-order controllers." Eastern-European Journal of Enterprise Technologies 6, no. 5 (126) (2023): 26–35. http://dx.doi.org/10.15587/1729-4061.2023.293206.

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The research focused on two-mass electromechanical systems widely utilized in industry. The challenge addressed in this work was to improve the synthesis of controllers for such systems to simplify it and enhance the quality of transition processes. Traditionally, the synthesis of control system loops for these systems was carried out using integer controllers and standard forms. However, this approach led to the synthesis of complex integer controllers that are difficult to implement. To overcome this issue, an original approach to the synthesis of control system loops based on the fractional

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43

Peruzzi, NJ, FR Chavarette, JM Balthazar, AM Tusset, ALPM Perticarrari, and RMFL Brasil. "The dynamic behavior of a parametrically excited time-periodic MEMS taking into account parametric errors." Journal of Vibration and Control 22, no. 20 (2016): 4101–10. http://dx.doi.org/10.1177/1077546315573913.

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Micro-electromechanical systems (MEMS) are micro scale devices that are able to convert electrical energy into mechanical energy or vice versa. In this paper, the mathematical model of an electronic circuit of a resonant MEMS mass sensor, with time-periodic parametric excitation, was analyzed and controlled by Chebyshev polynomial expansion of the Picard interaction and Lyapunov-Floquet transformation, and by Optimal Linear Feedback Control (OLFC). Both controls consider the union of feedback and feedforward controls. The feedback control obtained by Picard interaction and Lyapunov-Floquet tra

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44

Xing, Wei W., Ming Cheng, Kaiming Cheng, Wei Zhang, and Peng Wang. "InfPolyn, a Nonparametric Bayesian Characterization for Composition-Dependent Interdiffusion Coefficients." Materials 14, no. 13 (2021): 3635. http://dx.doi.org/10.3390/ma14133635.

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Composition-dependent interdiffusion coefficients are key parameters in many physical processes. However, finding such coefficients for a system with few components is challenging due to the underdetermination of the governing diffusion equations, the lack of data in practice, and the unknown parametric form of the interdiffusion coefficients. In this work, we propose InfPolyn, Infinite Polynomial, a novel statistical framework to characterize the component-dependent interdiffusion coefficients. Our model is a generalization of the commonly used polynomial fitting method with extended model ca

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45

Maillet, Denis, Célien Zacharie, and Benjamin Rémy. "Identification of an impulse response through a model of ARX structure." Journal of Physics: Conference Series 2444, no. 1 (2023): 012002. http://dx.doi.org/10.1088/1742-6596/2444/1/012002.

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Abstract Polynomial parametric models of ARX structure are becoming increasingly popular for characterizing heat transfer for linear thermal systems with time invariant coefficients. This stems from their robustness when applied to inverse problems, either for model reduction, for experimental model identification or for inverse input problems. Their parsimonious character allows to get residuals of very low levels with a limited number of coefficients. This paper shows, on a theoretical algebraic basis, that ARX models can be deduced from convolutive models.

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46

Kantarakias, Kyriakos Dimitrios, and George Papadakis. "Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems." Algorithms 13, no. 4 (2020): 90. http://dx.doi.org/10.3390/a13040090.

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In this paper, we consider the effect of stochastic uncertainties on non-linear systems with chaotic behavior. More specifically, we quantify the effect of parametric uncertainties to time-averaged quantities and their sensitivities. Sampling methods for Uncertainty Quantification (UQ), such as the Monte–Carlo (MC), are very costly, while traditional methods for sensitivity analysis, such as the adjoint, fail in chaotic systems. In this work, we employ the non-intrusive generalized Polynomial Chaos (gPC) for UQ, coupled with the Multiple-Shooting Shadowing (MSS) algorithm for sensitivity analy

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47

Mykhailenko, Oleksii. "Modeling and simulating dynamics of lithium-ion batteries using block-oriented models with piecewise linear static nonlinearity." E3S Web of Conferences 280 (2021): 05004. http://dx.doi.org/10.1051/e3sconf/202128005004.

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The article deals with the research of the efficiency of modelling the dynamics of voltage change in lithium-ion rechargeable batteries in charging/discharging modes using nonlinear block-oriented systems. Drawing on experimental data, a structural and parametric identification of the Hammerstein, Wiener and Hammerstein-Wiener models with a polynomial structure of the linear dynamic block and piecewise linear static nonlinearities was performed. It has been established that the best modelling accuracy was ensured by using the Hammerstein-Wiener system with a linear model having the 6th order o

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48

Li, Xiaoxue, and Xiaorong Hou. "Design of Parametric Controller for Two-Dimensional Polynomial Systems Described by the Fornasini-Marchesini Second Model." IEEE Access 7 (2019): 44070–79. http://dx.doi.org/10.1109/access.2019.2906272.

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49

Li, G., B. S. Mordukhovich, T. T. A. Nghia, and T. S. Phạm. "Error bounds for parametric polynomial systems with applications to higher-order stability analysis and convergence rates." Mathematical Programming 168, no. 1-2 (2016): 313–46. http://dx.doi.org/10.1007/s10107-016-1014-6.

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Shen, Dongying E., Sergio Lucia, Yiming Wan, Rolf Findeisen, and Richard D. Braatz. "Polynomial Chaos-Based H 2 -optimal Static Output Feedback Control of Systems with Probabilistic Parametric Uncertainties." IFAC-PapersOnLine 50, no. 1 (2017): 3536–41. http://dx.doi.org/10.1016/j.ifacol.2017.08.949.

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