Dynamic Lyapunov Machine Learning Control of Nonlinear Magnetic Levitation System

Abstract

This paper presents a novel dynamic deep learning architecture integrated with Lyapunov control to address the timing latency and constraints of deep learning. The dynamic component permits the network depth to increase or decrease depending on the system complexity/nonlinearity evaluated through the parameterized complexity method. A correlation study between the parameter tuning effect on the error is also made thus causing a reduction in the deep learning time requirement and computational cost during the network training and retraining process. The control Lyapunov function is utilized as an input cost function to the DNN in order to determine the system stability. A relearning process is triggered to account for the introduction of disturbances or unknown model dynamics, therefore, eliminating the need for an observer-based approach. The introduction of the relearning process also allows the algorithm to be applicable to a wider array of cyber–physical systems (CPS). The intelligent controller autonomy is evaluated under different circumstances such as high frequency nonlinear reference, reference changes, or disturbance introduction. The dynamic deep learning algorithm is shown to be successful in adapting to such changes and reaching a safe solution to stabilize the system autonomously.

Keywords

• magnetic levitation
• cyber–physical system
• CPS
• Lyapunov control
• deep learning
• energy harvesting