Nonlinear Non-Gaussian Density Steering with Input and Noise Channel Mismatch: Sinkhorn with Memory for Solving the Control-affine Schrodinger Bridge Problem

arXiv:2604.23370v1 Announce Type: cross Abstract: Solutions to the Schrodinger bridge problem and its generalizations yield feedback control policies for optimal density steering over a controlled diffusion. To numerically compute the same, the dynamic Sinkhorn recursion has become a standard approach. The mathematical engine behind this approach is the Hopf-Cole transform that recasts the conditions for optimality into a system of boundary-coupled linear PDEs. Recent works pointed out that for the control-affine Schrodinger bridge problem, this exact linearity via Hopf-Cole transform, and thus the standard Sinkhorn recursion, apply only if the control and noise channels are proportional. When the channels do not match, the Hopf-Cole-transformed PDEs remain nonlinear, and no algorithm is available to solve the same. We advance the state-of-the-art by designing a Sinkhorn recursion with memory that leverages the structure of these nonlinear PDEs, and demonstrate how it solves the control-affine Schrodinger bridge problem with input and noise channel mismatch. We prove the local stability of the proposed algorithm.

Related

• Optimal Stability of KL Divergence under Gaussian Perturbations
• Unifying Controller Design for Stabilizing Nonlinear Systems with Norm-Bounded Control Inputs
• Planning Under Observation Mismatch for Traffic Signal Control via Adaptive Modular World Models
• Model Predictive Control of Hybrid Dynamical Systems
• A Systematic Review and Taxonomy of Reinforcement Learning-Model Predictive Control Integration for Linear Systems

Source: arXiv cs.AI | 2026-04-28