Nonlinear System Identification Based on a Fock Space Framework.

Abstract

A method is presented for the identification of a nonlinear system represented by an operator V:E yields Y, where the input space E is a separable Hilbert space over the field of complex numbers and the output space Y is the Sobolev space H(n)-squared of complex-valued functions y on an interval I of the real line such that dky/dtk, k=O,...,n-1, are absolutely continuous and dny/dtn and element of L-squared (I). The above developments permit us to obtain the solution to our nonlinear system identification problem as the solution to an appropriate minimum norm problem in B(n)-squared (I.F sub rho(E)). Procedures for obtaining both the noncausal and causal solutions are given. We also introduce the concept of 'epsilon-causality', which is weaker than that of causality, and derive an epsilon-causal solution to our problem. The case when measurement errors are present is finally considered.The results are illustrated by the computer simulation of a simple example in which very good agreement with the theory is obtained over a wide time-interval.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1979
Accession Number
ADA071063

Entities

People

  • L. V. Zyla
  • Rui J. P. De Figueiredo

Organizations

  • Rice University

Tags

Communities of Interest

  • Counter IED

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Banach Space
  • Complex Numbers
  • Computer Simulations
  • Differential Equations
  • Equations
  • Hilbert Space
  • Information Science
  • Linear Systems
  • New York
  • Nonlinear Systems
  • Numbers
  • Sequences
  • Simulations
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space