Controlled SA-NODEs uniformly approximate trajectories of nonlinear controlled systems on compact sets and preserve approximate controllability, with error O(P^{-1/2} + Q^{-1/2}) under Sobolev and Barron regularity.
arXiv preprint arXiv:2012.02414 , year=
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A technique plants exact fixed points in Neural-ODE velocity fields with a rigorous proof that universality is preserved under local constraints.
Proves exponential turnpike and one-sided sparsity for L1-regularized optimal control of SA-NODEs, confirmed numerically on oscillators with 30x parameter reduction.
citing papers explorer
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Approximation and Controllability of Nonlinear Control-Affine Systems via Semiautonomous Neural Ordinary Differential Equations
Controlled SA-NODEs uniformly approximate trajectories of nonlinear controlled systems on compact sets and preserve approximate controllability, with error O(P^{-1/2} + Q^{-1/2}) under Sobolev and Barron regularity.
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Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality
A technique plants exact fixed points in Neural-ODE velocity fields with a rigorous proof that universality is preserved under local constraints.
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Turnpike and Sparse Optimal Control for Semiautonomous Neural ODEs
Proves exponential turnpike and one-sided sparsity for L1-regularized optimal control of SA-NODEs, confirmed numerically on oscillators with 30x parameter reduction.