AI Pontryagin or: How Artificial Neural Networks Learn to Control Dynamical Systems

The efficient control of complex dynamical systems has many applications in the natural and applied sciences. In most real-world control problems, control energy and cost constraints play a significant role. Although such optimal control problems can be formulated within the framework of variational calculus, their solution for complex systems is often analytically and computationally intractable. To overcome this outstanding challenge, we present AI Pontryagin, a versatile neural ordinary-differential-equation-based control framework that automatically learns control signals that steer high-dimensional dynamical systems towards a desired target state within a predefined amount of time. We demonstrate the ability of AI Pontryagin to learn control signals that closely resemble those found by corresponding optimal control frameworks in terms of control energy and deviation from the desired target state. Our results suggest that AI Pontryagin is capable to solve a wide range of control and optimization problems, including those that are analytically intractable.