Comparison of Deep Learning and Deterministic Algorithms for Control Modeling.

Area of Science:

• Engineering
• Control Theory
• Machine Learning

Background:

• Controlling nonlinear dynamics is crucial in many engineering applications.
• The van der Pol system is a common model for studying nonlinear oscillations.
• Comparing traditional control methods with machine learning approaches is essential for advancing control strategies.

Purpose of the Study:

• To model and compare the control of a forced van der Pol system using Physics-Informed Neural Networks (PINN) against benchmark methods.
• To evaluate controller performance in implementing circular trajectories in the system's state space.
• To investigate the impact of varying nonlinearities on different control schemes.

Main Methods:

• Utilized Physics-Informed Neural Networks (PINN) for modeling and control.
• Implemented benchmark controllers: idealized nonlinear feedforward (FF), linearized feedback (FB), and combined (C).
• Tested controllers on a designed benchmark problem with varying degrees of nonlinearity and trajectory amplitudes.

Main Results:

• PINN demonstrated good control performance with some stochasticity at higher nonlinearities.
• Idealized nonlinear FF control successfully converged to the desired trajectory.
• Linearized FB and combined C control methods failed, especially at unity nonlinear damping gain. PINN sometimes failed, becoming trapped in small-radius phases, while FF succeeded.
• PINN showed lower relative errors for varying trajectories but incurred a significantly higher computational burden (over 30x longer control time than FF).

Conclusions:

• PINN offers a viable, albeit computationally intensive, alternative for nonlinear system control.
• Traditional methods like idealized nonlinear FF can be effective but may struggle with complex nonlinearities.
• A comprehensive comparison of deterministic and machine learning approaches is vital for selecting appropriate controllers for future applications.