Wasserstein Proximal Algorithms for the Schrödinger Bridge Problem: Density Control With Nonlinear Drift

• Published in: IEEE transactions on automatic control Vol. 67; no. 3; pp. 1163 - 1178
• Main Authors: Caluya, Kenneth F., Halder, Abhishek
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Boundary conditions; Boundary value problems; Drift; Evolutionary computation; Fields (mathematics); Fixed points (mathematics); Gradient drift; Heuristic algorithms; Kernel; Mathematical analysis; mixed conservative–dissipative drift; Nonlinear control; Nonlinear dynamical systems; Nonlinear dynamics; Operators (mathematics); Optimal control; optimal mass transport (OMT); Optimized production technology; Partial differential equations; Probability density function; Probability density functions; Schrödinger bridge problem (SBP); State vectors; Steering; Uncertainty

In this article, we study the Schrödinger bridge problem (SBP) with nonlinear prior dynamics. In control-theoretic language, this is a problem of minimum effort steering of a given joint state probability density function (PDF) to another over a finite-time horizon, subject to a controlled stochasti...