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<p>Modern production processes frequently require steady-state analysis of continuous dynamic systems. Traditional numerical approaches, however, fall short in efficiency when tasked with addressing large-scale or dynamic problems. To tackle the inverse problem inherent in stability analysis, this study presents an innovative approach by integrating a combined excitation function into the foundational zeroing neural network (ZNN) model. This integration constrains the ZNN model, evolving it into an enhanced EZNN model specifically designed for solving the inverse of dynamic complex matrices. Additionally, this paper conducts a rigorous theoretical analysis of the robust performance of the EZNN model when excited by the combined function, both in the presence and absence of noise interference. The model solution process is promoted by using a class of high-dimensional continuous dynamic systems as an example, and numerical simulation experiments are used for validation. Considering the dynamic system satisfying 
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<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mo>{</mo> <mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><mi>A</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo>(</mo><mrow><mn>4</mn><mo>+</mo><mo>sin</mo><mo stretchy="false">(</mo><mn>2</mn><mi>t</mi><mo stretchy="false">)</mo><mi> </mi><mn>4</mn><mo>-</mo><mo>cos</mo><mo stretchy="false">(</mo><mn>2</mn><mi>t</mi><mo stretchy="false">)</mo><mi> </mi><mn>5</mn><mo>+</mo><mo>sin</mo><mo stretchy="false">(</mo><mn>2</mn><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>)</mo></mrow></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow><mi>C</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo>(</mo><mrow><mtable><mtr><mtd><mrow><mo>cos</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd><mtd><mrow><mo>sin</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd><mtd><mrow><mo>-</mo><mo>cos</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mo>-</mo><mo>sin</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd><mtd><mrow><mo>cos</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd><mtd><mrow><mo>sin</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr></mtable></mrow><mo>)</mo></mrow></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow><mi>b</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>4</mn><mo>+</mo><mo>cos</mo><mo stretchy="false">(</mo><mn>4</mn><mi>t</mi><mo stretchy="false">)</mo><mo>,</mo><mi>d</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mrow><mrow><mo stretchy="false">(</mo><mo>cos</mo><mo stretchy="false">(</mo><mn>2</mn><mi>t</mi><mo stretchy="false">)</mo><mo>,</mo><mo>cos</mo><mo stretchy="false">(</mo><mn>2</mn><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mrow><mi>T</mi></msup></mrow></mtd></mtr></mtable></mrow> </mrow></mrow></math>
<tex-math>\left\{ \matrix{ A(t) = \left( {4 + \sin (2t)\quad 4 - \cos (2t)\quad 5 + \sin (2t)} \right) \hfill \cr   C(t) = \left( {\matrix{{\cos (t)} &amp; {\sin (t)} &amp; { - \cos (t)}  \cr { - \sin (t)} &amp; {\cos (t)} &amp; {\sin (t)}  \cr } } \right) \hfill \cr b(t) = 4 + \cos (4t),d(t) = {(\cos (2t),\cos (2t))^T} \hfill \cr}  \right.</tex-math>
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, the error <italic>E</italic><sub>1</sub>(<italic>x</italic>(<italic>t</italic>),<italic>t</italic>) obtained by the EZNN model with combinatorial function excitation always remains negative or tends rapidly to 0. The <italic>x</italic> (<italic>t</italic>) obtained by the model converges rapidly to an exact solution of the system. Through the discussion of parametric conditions, it is also found that increasing the value of parameter γ increases the rate of convergence of the ZNN model.</p>
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Modern production processes frequently require steady-state analysis of continuous dynamic systems. Traditional numerical approaches, however, fall short in efficiency when tasked with addressing large-scale or dynamic problems. To tackle the inverse problem inherent in stability analysis, this study presents an innovative approach by integrating a combined excitation function into the foundational zeroing neural network (ZNN) model. This integration constrains the ZNN model, evolving it into an enhanced EZNN model specifically designed for solving the inverse of dynamic complex matrices. Additionally, this paper conducts a rigorous theoretical analysis of the robust performance of the EZNN model when excited by the combined function, both in the presence and absence of noise interference. The model solution process is promoted by using a class of high-dimensional continuous dynamic systems as an example, and numerical simulation experiments are used for validation. Considering the dynamic system satisfying 



{ A(t)=(4+sin(2t) 4-cos(2t) 5+sin(2t))C(t)=(cos(t)sin(t)-cos(t)-sin(t)cos(t)sin(t))b(t)=4+cos(4t),d(t)=(cos(2t),cos(2t))T 
\left\{ \matrix{ A(t) = \left( {4 + \sin (2t)\quad 4 - \cos (2t)\quad 5 + \sin (2t)} \right) \hfill \cr   C(t) = \left( {\matrix{{\cos (t)} & {\sin (t)} & { - \cos (t)}  \cr { - \sin (t)} & {\cos (t)} & {\sin (t)}  \cr } } \right) \hfill \cr b(t) = 4 + \cos (4t),d(t) = {(\cos (2t),\cos (2t))^T} \hfill \cr}  \right.


, the error E1(x(t),t) obtained by the EZNN model with combinatorial function excitation always remains negative or tends rapidly to 0. The x (t) obtained by the model converges rapidly to an exact solution of the system. Through the discussion of parametric conditions, it is also found that increasing the value of parameter γ increases the rate of convergence of the ZNN model.

Application of zeroed neural networks to stability analysis of continuous dynamic systems

College of Computer Science and Engineering

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Modern production processes frequently require steady-state analysis of continuous dynamic systems. Traditional numerical approaches, however, fall short in...

Application of zeroed neural networks to stability analysis of continuous dynamic systems

Published Online: Jul 02, 2024

Page range: -

Received: Mar 13, 2024

Accepted: May 27, 2024

DOI: https://doi.org/10.2478/amns-2024-1568

Keywords
Steady-state analysis, Continuous dynamical systems, Zeroized neural networks, Combined excitation functions, Dynamic complex matrix inverse

© 2024 Yun Huang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Application of zeroed neural networks to stability analysis of continuous dynamic systems

Published Online: Jul 02, 2024

Page range: -

Received: Mar 13, 2024

Accepted: May 27, 2024

DOI: https://doi.org/10.2478/amns-2024-1568

KeywordsSteady-state analysis, Continuous dynamical systems, Zeroized neural networks, Combined excitation functions, Dynamic complex matrix inverse

© 2024 Yun Huang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Steady-state analysis, Continuous dynamical systems, Zeroized neural networks, Combined excitation functions, Dynamic complex matrix inverse