The paper defines robust invertibility for nonlinear dynamics using contraction and bi-Lipschitzness, and constructs biLipREN, a recurrent equilibrium network whose forward and inverse are both contracting and bi-Lipschitz by construction.
Iterative learning control of nonlinear non-minimum phase systems and its application to system and model inversion,
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Robustly Invertible Nonlinear Dynamics and the BiLipREN: Contracting Neural Models with Contracting Inverses
The paper defines robust invertibility for nonlinear dynamics using contraction and bi-Lipschitzness, and constructs biLipREN, a recurrent equilibrium network whose forward and inverse are both contracting and bi-Lipschitz by construction.