Discrete Bidirectional Associative Memory Neural Networks of the Cohen–Grossberg Type for Engineering Design Symmetry Related Problems: Practical Stability of Sets Analysis

In recent years, artificial intelligence techniques have become fundamental parts of various engineering research activities and practical realizations. The advantages of the neural networks, as one of the main artificial intelligence methods, make them very appropriate for different engineering des...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 2; p. 216
Main Author Stamov, Trayan
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.02.2022
Subjects
Artificial intelligence
Associative memory
BAM neural networks
Cohen–Grossberg types
Criteria
Design engineering
Design optimization
Designers
engineering design
Engineering research
Industrial design
Investigations
Liapunov functions
Neural networks
Pattern recognition
practical stability of sets
Recurrent neural networks
Regularization methods
Stability analysis
symmetries
Symmetry
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Summary:In recent years, artificial intelligence techniques have become fundamental parts of various engineering research activities and practical realizations. The advantages of the neural networks, as one of the main artificial intelligence methods, make them very appropriate for different engineering design problems. However, the qualitative properties of the neural networks’ states are extremely important for their design and practical performance. In addition, the variety of neural network models requires the formulation of appropriate qualitative criteria. This paper studies a class of discrete Bidirectional Associative Memory (BAM) neural networks of the Cohen–Grossberg type that can be applied in engineering design. Due to the nature of the proposed models, they are very suitable for symmetry-related problems. The notion of the practical stability of the states with respect to sets is introduced. The practical stability analysis is conducted by the method of the Lyapunov functions. Examples are presented to verify the proposed criteria and demonstrate the efficiency of the results. Since engineering design is a constrained processes, the obtained stability of the sets’ results can be applied to numerous engineering design tasks of diverse interest.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14020216