i-LiftProj: Spectrally Normalized Invertible Koopman Lifting for First-Order Nonlinear Optimal Control

초록

This letter presents i-LiftProj, a first-order optimization framework for nonlinear optimal control based on a spectrally normalized invertible Koopman lifting. Building on the recently proposed LiftProj framework, which performs ADMM dynamics projections in a lifted linear space, we replace the unconstrained autoencoder with an augmented Invertible ResNet whose ambient lifting map is bi-Lipschitz by construction. We also replace the learned decoder with a fixed-point inverse of the learned ambient diffeomorphism, thereby removing learned-decoder approximation error from the projection step. Since the lifted linear model remains approximate, we analyze i-LiftProj through a surrogate dynamics manifold induced by the learned lifting rather than identifying it with the true nonlinear dynamics manifold. Under standard smoothness and strong-convexity assumptions on the convex ADMM subproblem, we derive an asymptotic residual-floor bound whose size is explicitly controlled by the lifting condition number and by the mismatch between the true dynamics manifold and its lifted linear surrogate. Numerical experiments on a 6-DoF rocket powered descent guidance problem show that i-LiftProj preserves solution quality and constraint satisfaction while yielding smoother residual reduction than the LiftProj baseline.

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