The Volterra Series for Modeling of Input-Output Dynamical Systems
Year: 1999 Authors: Denis N. Sidorov
Core claim
Volterra kernels can be uniquely recovered from linear combinations of system responses under suitable test perturbations, with existence conditions for a unique continuous solution established.
Topics
Volterra series, input-output dynamical systems, integral equations, system identification
Domains
functional analysis, integral equations, system theory, kernel identification
Methods
finite Volterra sums, test perturbations, linear combinations of reactions, software modeling
Media
software, heat-exchange process models
Paper text
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BRIDGES Mathematical Connections in Art, Music, and Science
The Volterra Series for Modeling of Input-Output Dynamical Systems
Denis N. Sidorov Energy Systems Institute of SB RAS Irkutsk, 664033, Russia E-mail: ill_posed@ISEM.SEI.IRK.RU
It is known that many natural processes can be described by dynamic systems. For modeling of dynamic systems of entry-exit type, the Volterra series are used. The finite sums of series are applied. Our aim is to identify the Volterra kernels (transfer functions) by special responses of the system to the special sets of test perturbations. This problem is solved by the reduction of this problem to the multidimensional Volterra integral equations of the kind via the linear combinations of reactions. The necessary and sufficient conditions of existence of the unique continuous solution of these equations are given. The software for modeling of the heat-exchange processes was created by this base.