Infinite-Horizon Sparse Optimal Control: Solution through a Finite-Horizon Subproblem and Its Receding-Horizon Implementation

What the math gives to ML

The paper gives a constructive reduction of an infinite-horizon L1 sparse-control problem to a finite-horizon problem. Its key mechanism is spectral separation: after the anti-stable component has been eliminated, the remaining stable state decays without further input, so an optimal control has finite support. This can transfer to adaptive-depth recurrent or iterative neural modules by learning sparse residual corrections only while unstable hidden-state components remain. The engineering value is a stopping rule tied to an estimated Jacobian spectrum rather than an arbitrary maximum depth.