DocumentCode :
1182958
Title :
A best approximation framework and implementation for simulation of large-scale nonlinear systems
Author :
de Figueiredo, Rui J.P. ; Dwyer, Thomas A W, III
Volume :
27
Issue :
11
fYear :
1980
fDate :
11/1/1980 12:00:00 AM
Firstpage :
1005
Lastpage :
1014
Abstract :
A conceptual and mathematical framework is presented for optimally approximating a large-scale continuous-time-parameter nonlinear dynamical system S_C by a continuous-time-parameter model \\hat{S}_C as well as a discrete-time-parameter model \\hat{S}_D , which can be readily simulated respectively on an analog and on a digital computer. A reproducing kernel Hilbert space approach in appropriate weighted Fock spaces is used in the problem formulation and solution. Assuming that the input-output map of the system S_C can be represented by a Volterra functional series V_t , belonging to a Fock space F_{\\underline {\\rho}}(E) , the input-output maps for the simulators \\hat{S}_C and \\hat{S}_D are obtained as "best approximations" in F_{\\underline {\\rho}}(E) for the entire (untruncated) series V_t . Each of these models has the following features: (a) It is adaptive because it is based on a set of test input-output pairs which can be incorporated in the system by on-line multiplexing, (b) it is optimal in the sense of being a projection in a Hilbert space of nonlinear operators, (c) it is easily implementable by means of a set of interconnected linear dynamical systems and zero-memory nonlinear functions of single variables, and (d) unlike polynomic (truncated Volterra series) approximations, it constitutes a global approximation and thus is valid under both small- and large-signal operating conditions.
Keywords :
General nonlinear theory; Large-scale systems; Nonlinear systems, continuous-time; Analog computers; Computational modeling; Computer simulation; Hilbert space; Kernel; Large-scale systems; Mathematical model; Nonlinear dynamical systems; Nonlinear systems; System testing;
fLanguage :
English
Journal_Title :
Circuits and Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
0098-4094
Type :
jour
DOI :
10.1109/TCS.1980.1084741
Filename :
1084741
Link To Document :
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