AI Pontryagin or how artificial neural networks learn to control dynamical systems

Area of Science:

• Control Theory
• Applied Mathematics
• Machine Learning

Background:

• Optimal control problems for complex dynamical systems are crucial in science and engineering.
• Real-world applications often involve significant control energy and cost constraints.
• Analytical and computational intractability hinders solving these problems for high-dimensional systems.

Purpose of the Study:

• To present AI Pontryagin, a novel framework for controlling complex dynamical systems.
• To develop an automated method for learning control signals that respect energy and cost constraints.
• To address the limitations of traditional optimal control methods for intractable systems.

Main Methods:

• Utilizing neural ordinary differential equations (NODEs) within a versatile control framework.
• Developing an AI-driven approach to automatically learn control signals.
• Steering high-dimensional dynamical systems towards a specified target state within a defined time.

Main Results:

• AI Pontryagin successfully learns control signals for complex dynamical systems.
• Learned control signals closely match those from traditional optimal control frameworks regarding energy and state deviation.
• Demonstrated capability in solving analytically intractable control and optimization problems.

Conclusions:

• AI Pontryagin offers an effective solution for complex dynamical system control.
• The framework shows promise for a wide array of control and optimization applications.
• It overcomes limitations of traditional methods for computationally challenging problems.