Paper Info
Title
Convergence of Dynamic Programming on the Semidefinite Cone for Discrete-Time Infinite-Horizon LQR
Abstract
The goal of this article is to investigate new and simple convergence analysis of dynamic programming for the 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -value iteration, the policy iteration always converges exponentially fast. An example is given to illustrate the results.
Year
DOI
Venue
2022
10.1109/TAC.2022.3181752
IEEE Transactions on Automatic Control
Keywords
DocType
Volume
Convergence,dynamic programming,linear time-invariant (LTI) system,optimal control,reinforcement learning
Journal
67
Issue
ISSN
Citations 
10
0018-9286
0
PageRank 
References 
Authors
0.34
12
1
Name
Order
Citations
PageRank
Donghwan Lee1259.30