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Related Concept Videos

First Order Systems01:21

First Order Systems

First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
Neural Circuits01:25

Neural Circuits

Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
Classification of Systems-II01:31

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

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Related Experiment Video

Updated: Jul 7, 2026

DeepOmicsAE: Representing Signaling Modules in Alzheimer's Disease with Deep Learning Analysis of Proteomics, Metabolomics, and Clinical Data
09:47

DeepOmicsAE: Representing Signaling Modules in Alzheimer's Disease with Deep Learning Analysis of Proteomics, Metabolomics, and Clinical Data

Published on: December 15, 2023

High-order neural network structures for identification of dynamical systems.

E B Kosmatopoulos1, M M Polycarpou, M A Christodoulou

  • 1Dept. of Electron. and Comput. Eng., Tech. Univ. of Crete, Chania.

IEEE Transactions on Neural Networks
|January 1, 1995
PubMed
Summary

This study explores high-order neural networks for dynamical system identification. These networks offer improved approximation capabilities and stable learning algorithms for complex engineering problems.

Related Experiment Videos

Last Updated: Jul 7, 2026

DeepOmicsAE: Representing Signaling Modules in Alzheimer's Disease with Deep Learning Analysis of Proteomics, Metabolomics, and Clinical Data
09:47

DeepOmicsAE: Representing Signaling Modules in Alzheimer's Disease with Deep Learning Analysis of Proteomics, Metabolomics, and Clinical Data

Published on: December 15, 2023

Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Dynamical Systems

Background:

  • Recurrent neural networks (RNNs) are widely used in engineering.
  • A key challenge is developing stable and efficient learning algorithms for RNNs.
  • High-order neural networks (HONNs) offer a potential solution.

Purpose of the Study:

  • To investigate the approximation and learning properties of high-order neural networks.
  • To apply these networks to the identification of dynamical systems.
  • To design and analyze identification schemes using HONN architectures.

Main Methods:

  • Studied approximation and learning properties of recurrent high-order neural networks.
  • Incorporated dynamic neurons within the network architecture.
  • Developed and analyzed identification schemes based on HONNs.

Main Results:

  • Demonstrated that HONNs with sufficient high-order connections can approximate arbitrary dynamical systems.
  • Showcased the effectiveness of HONN architectures for system identification.
  • Developed stable and efficient learning algorithms for these networks.

Conclusions:

  • Recurrent high-order neural networks are powerful tools for approximating complex dynamical systems.
  • HONN architectures provide a viable approach for stable and efficient system identification.
  • Further research into HONNs can advance the field of dynamical system modeling.