Gradient Flow Algorithms for Density Propagation in Stochastic Systems

• Published in: IEEE transactions on automatic control Vol. 65; no. 10; pp. 3991 - 4004
• Main Authors: Caluya, Kenneth F., Halder, Abhishek
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Continuity (mathematics); Fokker–Planck–Kolmogorov (FPK) equation; Free energy; Function approximation; gradient descent; Gradient flow; Handheld computers; Iterative methods; Manifolds; Mathematical analysis; Measurement; Nonlinear control; Nonlinear systems; Optimal control; optimal transport; Partial differential equations; Probability density function; Probability density functions; Propagation; proximal operator; Regularization; Stochastic processes; Stochastic systems; Transient analysis; Uncertainty; uncertainty propagation

We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the transient joint PDFs subject to prior dynamics arises in uncert...