Approximate Feedback Linearization for a Nonlinear Hyperbolic PDE Class -- Part I: Volterra Truncation

What the math gives to ML

The paper gives a constructive way to replace an infinite nonlinear feedback-linearizing transformation with a finite Volterra polynomial while retaining local stability because omitted higher-order terms vanish near the equilibrium. The transferable asset is an order-controlled representation of causal nonlinear memory, not the PDE-specific backstepping kernel itself. This suggests augmenting a stable recurrent or state-space transition with quadratic or cubic lag-product terms that cancel dominant nonlinear feedback. Truncation order becomes an explicit accuracy-versus-compute knob, and the method is falsifiable through long-horizon stability and rollout experiments.