Transfer Functions for Nonlinear Systems via Fourier-Borel Transforms.
Abstract
An analytical functional expansions which we shall call Fliess's generalized expansions. These nonlinear functional expansions are analogous to Fourier series or integral expansions of response functions of linear systems. The shuffle product which is the characteristic of the noncommutative algebra introduced plays a very significant role in this approach. Moreover what makes this approach more attractive is the possibility of doing all of the noncommutative algebra on a computer in any of the currently available symbolic programming languages such as Macsyma, Reduce, PL1, and Lisp. Nonlinear functional expansions for the solution of nonlinear ordinary differential equations can be summarized by the newly introduced Laplace-Borel transforms. Some properties of these transforms were previously obtained. Some further properties will be given in this paper. The main theorem of the paper gives the transform of the response of the nonlinear system as a Cauchy product of its transfer function which is introduced for the first time here and the transform of the input function of the system together with memory effects. Applications of this new transfer-function approach are given using nonlinear electronic circuits. Two categories of applications are presented, namely, analysis of circuits, and synthesis of circuits. Various other examples can be given from other nonlinear dynamical systems; for example nonlinear aerodynamics, nonlinear flight mechanics in which cases these two classes of problems can be called either direct problems or inverse problems. Keywords: Transfer function, Linear systems, Fourier-Borel transforms.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1988
- Accession Number
- ADA198485
Entities
People
- Aynur Uenal
- Suemer Can
Organizations
- Ames Research Center