Data-driven learning of non-autonomous systems

Understand

We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs.

• To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances.
• The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances.
• This transforms the original system into a piecewise parametric system that is locally time invariant.