L∞ analysis and state-feedback control of Hopfield networks

Area of Science:

• Control Systems Engineering
• Computational Neuroscience
• Nonlinear Dynamics

Background:

• Nonsymmetric Hopfield networks are relevant for modeling complex behaviors in visuo-motor control loops.
• Analyzing these networks under bounded disturbances is crucial for understanding their stability and performance.
• Existing methods may not fully capture the dynamics of these systems.

Purpose of the Study:

• To analyze the induced L∞ gain of generalized Hopfield networks with bounded disturbances.
• To design a state-feedback control for achieving L∞-type performance in these networks.
• To provide a framework for mimicking complex behaviors in visuo-motor control using engineered networks.

Main Methods:

• Utilizing the Lur'e-Postnikov systems approach for stability analysis.
• Applying state-feedback control design techniques.
• Employing numerical simulations to validate the proposed control strategy.

Main Results:

• The Lur'e-Postnikov approach successfully characterizes the L∞ gain of the considered Hopfield networks.
• A state-feedback controller is designed to guarantee the desired L∞ performance.
• Numerical examples demonstrate the effectiveness of the control design.

Conclusions:

• The proposed method offers a robust approach to controlling nonsymmetric Hopfield networks in the presence of disturbances.
• This work contributes to the understanding and application of Hopfield networks in complex control systems.
• The findings have implications for the development of advanced visuo-motor control systems.