A Theoretical Difficulty in Approximate Dynamic Programming with Input Constraints
Abstract
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional constrained ADP framework, the optimal control issearched via a policy iteration algorithm, where the value under a constrainedcontrol is solved from a Hamilton-Jacobi-Bellman (HJB) equation while theconstrained control policy is improved based on the current estimated value.This concise and applicable method has been widely-used. However, the con-vergence of the existing policy iteration algorithm may possesses a theoreticaldifficulty, which might be caused by forcibly evaluating the same trajectoryeven though the control policy has already changed. This problem will beexplored in this paper.
Cite
@article{arxiv.1805.06424,
title = {A Theoretical Difficulty in Approximate Dynamic Programming with Input Constraints},
author = {Xuefeng Bao and Zhi-Hong Mao and Nitin Sharma},
journal= {arXiv preprint arXiv:1805.06424},
year = {2018}
}
Comments
The theoretical difficulty talked in this paper is too minor. It does not affect the final result in the original paper. And, my presentation is also problematic. Sorry for that