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Complete memory structures for approximating nonlinear discrete-time mappings.

B W Stiles1, I W Sandberg, J Ghosh

  • 1Dept. of Electr. and Comput. Eng., Texas Univ., Austin, TX.

IEEE Transactions on Neural Networks
|January 1, 1997
PubMed
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This study presents a novel two-stage structure for approximating nonlinear discrete-time systems. A "complete memory" concept is introduced, enabling accurate modeling of complex system dynamics for artificial neural network design.

Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Computational Neuroscience

Background:

  • Nonlinear discrete-time systems are prevalent in various scientific and engineering fields.
  • Accurate modeling of these systems is crucial for analysis and control.
  • Existing modeling structures may have limitations in capturing complex dynamics.

Purpose of the Study:

  • To introduce a general, two-stage structure for approximating nonlinear discrete-time systems.
  • To define and utilize the concept of "complete memory" for enhanced modeling capabilities.
  • To provide a template for designing artificial neural networks for spatiotemporal processing.

Main Methods:

  • A two-stage structure comprising a dynamical stage and a memoryless nonlinear stage.

Related Experiment Videos

  • Development of a theorem establishing necessary and sufficient conditions for modeling capability.
  • Introduction and application of the "complete memory" concept.

    • Main Results:

    • A theorem proves that specific structures with a "complete memory" dynamical stage can approximate a wide class of nonlinear discrete-time systems.
    • Demonstration that bounded-input bounded-output, time-invariant, causal memory structures approximate system dynamics if and only if they possess "complete memory".
    • Presentation of linear and nonlinear examples of "complete memory" structures.

    Conclusions:

    • The proposed "complete memory" structure offers a powerful and general approach to modeling nonlinear discrete-time systems.
    • This structure serves as a foundational template for developing advanced artificial neural networks tailored for nonlinear spatiotemporal data processing.
    • The findings advance the theoretical understanding of system approximation and provide practical design guidelines.