Model predictive control of nonlinear dynamical systems based on long sequence stable Koopman network.

Area of Science:

• Control Theory
• Machine Learning
• Nonlinear Dynamics

Background:

• Koopman methods transform nonlinear systems into linear ones using high-dimensional mapping.
• Deep learning-based Koopman methods face challenges with slow convergence and unstable long-term predictions.

Purpose of the Study:

• To develop a Stable Deep Koopman Network with Model Predictive Control (SDKN-MPC) for enhanced nonlinear control.
• To address the limitations of existing deep learning Koopman methods regarding convergence speed and prediction stability.

Main Methods:

• Utilized a Stable Koopman Solver Algorithm to derive a stable Koopman operator.
• Employed interleaved neural network training for embedding functions and Koopman operator until convergence.
• Integrated Model Predictive Control (MPC) with the Koopman operator for high-dimensional system control.
• Incorporated an auxiliary network to refine predictive control inputs.

Main Results:

• The SDKN-MPC method demonstrated rapid convergence.
• Achieved superior long-term prediction performance compared to existing deep learning methods.
• Successfully extracted more effective nonlinear features from control tasks.

Conclusions:

• The proposed SDKN-MPC method provides a stable and efficient approach for nonlinear control.
• SDKN-MPC offers significant improvements in predictive performance and convergence speed.
• This method advances the application of Koopman methods in complex control systems.