论文信息 - A philosophy for the modelling of realistic nonlinear systems

A philosophy for the modelling of realistic nonlinear systems

A nonlinear dynamical system is modelled as a nonlinear mapping from a set of input signals into a corresponding set of output signals. Each signal is specified by a set of real number parameters, but such sets may be uncountably infinite. For numerical simulation of the system each signal must be represented by a finite parameter set and the mapping must be defined by a finite arithmetical process. Nevertheless the numerical simulation should be a good approximation to the mathematical model. We discuss the representation of realistic dynamical systems and establish a stable approximation theorem for numerical simulation of such systems.

[1] Jan C. Willems,et al. Stability, Instability, Invertibility and Causality , 1969 .

[2] N. Wiener,et al. Fourier Transforms in the Complex Domain , 1934 .

[3] Vincent J. Bruno. A Weierstrass approximation theorem for topological vector spaces , 1984 .

[4] P. Falb,et al. A Generalized Transform Theory for Causal Operators , 1969 .

[5] P. M. Prenter. A Weierstrass theorem for real, separable Hilbert spaces , 1970 .

[6] Anatoli Torokhti,et al. A methodology for the constructive approximation of nonlinear operators defined on noncompact sets , 1997 .

[7] A. Torokhti,et al. Optimal fixed rank transform of the second degree , 2001 .

[8] G. Lewicki,et al. Approximation by Superpositions of a Sigmoidal Function , 2003 .

[9] B. Russell. I.—On the Notion of Cause , 1913 .

[10] Phil Howlett,et al. On the constructive approximation of non-linear operators in the modelling of dynamical systems , 1997 .

[11] Israel Gohberg,et al. Theory and Applications of Volterra Operators in Hilbert Space , 2004 .

[12] Anatoli Torokhti,et al. Weak interpolation and approximation of non-linear operators on the space C([0,1]) , 1998 .

[13] G. Alexits. Approximation theory , 1983 .

[14] Irving Segal,et al. CAUSALITY AND ANALYTICITY , 1955 .

[15] Irwin W. Sandberg,et al. Uniform approximation of multidimensional myopic maps , 1997 .

[16] Phil Howlett,et al. On the best quadratic approximation of nonlinear systems , 2001 .