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Nonlinear Stochastic Optimal Control with Input Saturation Constraints Based on Path Integrals
Author(s) -
Satoh Satoshi,
Kappen Hilbert J.
Publication year - 2020
Publication title -
ieej transactions on electrical and electronic engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.254
H-Index - 30
eISSN - 1931-4981
pISSN - 1931-4973
DOI - 10.1002/tee.23177
Subject(s) - constraint (computer aided design) , optimal control , stochastic control , nonlinear system , saturation (graph theory) , mathematical optimization , path (computing) , control theory (sociology) , path integral formulation , mathematics , bellman equation , control (management) , computer science , physics , quantum mechanics , combinatorics , artificial intelligence , programming language , quantum , geometry
Abstract This paper is concerned with a finite‐time nonlinear stochastic optimal control problem with input saturation as a hard constraint on the control input. The stochastic Hamilton‐Jacobi‐Bellman (SHJB) equation associated with this problem is derived, and a concrete solution method is also presented by extending an iteration framework of path integral stochastic optimal control. This is the first result that provides an optimal feedback control rigorously satisfying the saturation constraint as a solution to the SHJB equation. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.