Convolutional Neural Networks as Asymmetric Volterra Models Based on Generalized Orthonormal Basis Functions

Area of Science:

• Control Systems Engineering
• Machine Learning
• Dynamical Systems Theory

Background:

• Dynamical system modeling is crucial for understanding and controlling complex behaviors.
• Traditional methods for Volterra model identification can be computationally intensive and sensitive to noise.
• Generalized Orthonormal Basis Function (GOBF)-Volterra models offer a structured approach to nonlinear system representation.

Purpose of the Study:

• To introduce a novel Convolutional Neural Network (CNN) based approach for deriving Volterra models of dynamical systems.
• To demonstrate that CNNs can effectively learn system parameters, represented by the network's weights.
• To validate the proposed method's accuracy and robustness in the presence of noise and its applicability to real-world systems.

Main Methods:

• A Convolutional Neural Network (CNN) architecture was designed to process system input-output data.
• The CNN was trained to derive the parameters of a Generalized Orthonormal Basis Function (GOBF)-Volterra model.
• The learned weights of the CNN were shown to directly correspond to the system's poles.

Main Results:

• The CNN approach successfully recovered system parameters with high accuracy when no noise was present.
• Even with significant noise, the errors in the identified linear and nonlinear system parameters were minimal.
• The method was successfully applied to identify the dynamical model of a quadcopter using flight test data.

Conclusions:

• Convolutional Neural Networks provide a powerful and accurate tool for Volterra model identification of dynamical systems.
• The proposed CNN-based method offers a robust alternative to traditional system identification techniques, particularly in noisy environments.
• This approach demonstrates significant potential for real-world applications in areas such as robotics and control engineering.