@article{Tan2023, 
author = {Xufeng Tan and Yuan Li and Yang Liu},
title = {Stochastic linear quadratic optimal tracking control for discrete-time systems with delays based on Q-learning algorithm},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {5},
pages = {10249-10265},
keywords = {reinforcement Q-learning, value iterative, model-free, stochastic linear quadratic optimal tracking, time delay, deterministic system},
url = {https://www.sciopen.com/article/10.3934/math.2023519},
doi = {10.3934/math.2023519},
abstract = {In this paper, a reinforcement Q-learning method based on value iteration (Ⅵ) is proposed for a class of model-free stochastic linear quadratic (SLQ) optimal tracking problem with time delay. Compared with the traditional reinforcement learning method, Q-learning method avoids the need for accurate system model. Firstly, the delay operator is introduced to construct a novel augmented system composed of the original system and the command generator. Secondly, the SLQ optimal tracking problem is transformed into a deterministic one by system transformation and the corresponding Q function of SLQ optimal tracking control is derived. Based on this, Q-learning algorithm is proposed and its convergence is proved. Finally, a simulation example shows the effectiveness of the proposed algorithm.}
}