Diagonal Kernel Point Estimation of nth-Order Discrete Volterra-Wiener Systems

Diagonal Kernel Point Estimation of nth-Order Discrete Volterra-Wiener Systems

The estimation of diagonal elements of a Wiener model kernel is a well known practical and theoretical problem. The new operators and notations here proposed aim at the automatic code generation for the implementation of efficient and accurate nonparametric algorithms for the identification of diagonal points. The resulting formulas here presented allow the direct implementation of the Wiener k...

Discrete Volterra Equations - Discrete Volterra Operators, Fixed Point Theorems & their Application

Positive Solutions for Systems of nth Order Three-point Nonlocal Boundary Value Problems

Intervals of the parameter λ are determined for which there exist positive solutions for the system of nonlinear differential equations, u(n) + λa(t)f(v) = 0, v(n)+λb(t)g(u) = 0, for 0 < t < 1, and satisfying three-point nonlocal boundary conditions, u(0) = 0, u(0) = 0, . . . , u(n−2)(0) = 0, u(1) = αu(η), v(0) = 0, v(0) = 0, . . . , v(n−2)(0) = 0, v(1) = αv(η). A Guo-Krasnosel’skii fixed point...

Kernel-based local order estimation of nonlinear nonparametric systems

Approach to Identification of a Second-Order Volterra Kernel of Nonlinear Systems by Tchebyshev Polynomials Method

In this study, we investigate the Tchebyshev polynomials expansion method for the kernels identification of nonlinear systems. In aerodynamic systems, all the output data to an arbitrary input may be obtained by executing the Computational Fluid Dynamic (CFD) program code. This calculation process may take more than several hours or days to complete. In comparison with the indicial or impulse m...