Abstract
The efficient control of complex dynamical systems has many applications in the natural and applied sciences. In most real-world control problems, both 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 control framework based on neural ordinary differential equations that automatically learns control signals that steer high-dimensional dynamical systems towards a desired target state within a specified time interval. 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 of solving a wide range of control and optimization problems, including those that are analytically intractable.
Highlights
The efficient control of complex dynamical systems has many applications in the natural and applied sciences
Before introducing the basic principles of AI Pontryagin, we first provide a mathematical formulation of the control problem of networked dynamical systems
The optimal control of networked dynamical systems is associated with minimizing a certain cost functional, e.g., the strength and frequency of a control signal, or, more generally, the control energy (2)
Summary
The efficient control of complex dynamical systems has many applications in the natural and applied sciences. In most real-world control problems, both control energy and cost constraints play a significant role 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 control framework based on neural ordinary differential equations that automatically learns control signals that steer high-dimensional dynamical systems towards a desired target state within a specified time interval. Even if a certain control policy is able to steer a system towards a target state, it may not be possible to implement it in practice because of resource[16] and energy[17] constraints. Achieving optimal control of networked dynamical systems is a central task in control theory[19]
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