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Two-Dimensional Parametric Polynomial Chaotic System
IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022When used in engineering applications, most existing chaotic systems may have many disadvantages, including discontinuous chaotic parameter ranges, lack of robust chaos, and easy occurrence of chaos degradation. In this article, we propose a two-dimensional (2-D) parametric polynomial chaotic system (2D-PPCS) as a general system that can yield many 2-D
Zhongyun Hua +3 more
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Polynomial Chaos Expansion for Parametric Problems in Engineering Systems: A Review
IEEE Systems Journal, 2020In engineering systems with uncertain parameters, it is crucial for system analysis and control to analyze the relationship between these uncertain parameters and system outputs (or states). Nevertheless, the acquisition of this parameter-output function, termed parametric problem in this article, is not easy because it is usually a complicated ...
Danfeng Shen +3 more
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Comprehensive Characteristic Decomposition of Parametric Polynomial Systems
Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation, 2021This paper presents an algorithm that decomposes an arbitrary set F of multivariate polynomials involving parameters into finitely many sets Γi of (lexicographical) Grobner bases G ij such that associated with each Γi there is a system Ai of parametric constraints, all the Ai's partition the parameter space, all the Gij's in each Γi remain Grobner ...
Rina Dong +3 more
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Analyzing Boolean Functions via Solving Parametric Polynomial Systems
Journal of Systems Science and Complexity, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Zhenyu, Sun, Yao, Lin, Dongdai
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Minimal polynomial systems for parametric matrices
Linear and Multilinear Algebra, 2012In this article, we study the minimal polynomials of parametric matrices. Using the concept of (comprehensive) Grobner systems for parametric ideals, we introduce the notion of a minimal polynomial system for a parametric matrix, i.e. we decompose the space of parameters into a finite set of cells and for each cell we give the corresponding minimal ...
Amir Hashemi +2 more
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A package for solving parametric polynomial systems
ACM Communications in Computer Algebra, 2010A new Maple package for solving parametric systems of polynomial equations and inequalities is described. The main idea for solving such a system is as follows. The parameter space Rd is divided into two parts: the discriminant variety W and its complement R d nW
Jürgen Gerhard +2 more
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Identifiability of Scalar Linearly Parametrized Polynomial Systems
IFAC Proceedings Volumes, 1991Abstract We present necessary and sufficient conditions for the identification of a vector θ of unknown parameters in scalar dynamical systems of the form x = f (x, θ) + g(x, u), where f(x, θ) is a polynomial function of the state x that is affine in θ, and g(x, u) is a polynomial in the state x and the input u.
S. Dasgupta +4 more
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Parametric and state estimation for nonlinear polynomial systems
2017 18th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), 2017This manuscript deals with parametric and state estimation problem of discrete-time nonlinear polynomials systems. In this respect, the aim is to design a Recursive State and Parametric Estimation (RSPE) algorithm, based on least square principle, polynomial adjustable models and Kalman filter theory.
Marai Ghanmi Afef +2 more
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Solving Parametric Polynomial Systems by RealComprehensiveTriangularize
2014In the authors’ previous work, the concept of comprehensive triangular decomposition of parametric semi-algebraic systems (RCTD for short) was introduced. For a given parametric semi-algebraic system, say S, an RCTD partitions the parametric space into disjoint semi-algebraic sets, above each of which the real solutions of S are described by a finite ...
Changbo Chen, Marc Moreno Maza
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Arithmetic Continuation of Regular Roots of Formal Parametric Polynomial Systems
Computational Optimization and Applications, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eaves, B. Curtis, Rothblum, Uriel G.
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