Convergence of Dynamic Programming on the Semidefinite Cone
Optimization and Control
2021-06-18 v1 Systems and Control
Systems and Control
Abstract
The goal of this paper is to investigate new and simple convergence analysis of dynamic programming for linear quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of both matrix inequalities and matrix norm. Under a mild assumption on the initial parameter, we prove that the Q-value iteration exponentially converges to the optimal solution. Moreover, a global asymptotic convergence is also presented. These results are then extended to the policy iteration. We prove that in contrast to the Q-value iteration, the policy iteration always converges exponentially fast. An example is given to illustrate the results.
Cite
@article{arxiv.2106.09391,
title = {Convergence of Dynamic Programming on the Semidefinite Cone},
author = {Donghwan Lee},
journal= {arXiv preprint arXiv:2106.09391},
year = {2021}
}