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A philosophy for the modelling of realistic nonlinear systems |
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| Authors: | Phil Howlett Anatoli Torokhti Charles Pearce |
| Affiliation: | Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes, SA 5095, Australia ; Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes, SA 5095, Australia. ; Department of Applied Mathematics, University of Adelaide, Adelaide, SA 5005, Australia |
| Abstract: | 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. |
| Keywords: | Operator approximation realistic nonlinear systems |
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