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

Abstract

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.