Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Method

Na Li, Xun Li, Jing Peng, Zuo Quan Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)


This article adopts a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where the drift and diffusion terms in the dynamics may depend on both the state and control. Based on the Bellman's dynamic programming principle, we presented an online RL algorithm to attain optimal control with partial system information. This algorithm computes the optimal control, rather than estimates the system coefficients, and solves the related Riccati equation. It only requires local trajectory information, which significantly simplifies the calculation process. We shed light on our theoretical findings using two numerical examples.

Original languageEnglish
Pages (from-to)5009-5016
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number9
Publication statusPublished - 1 Sept 2022


  • Linear quadratic (LQ) problem
  • reinforcement learning (RL)
  • stochastic optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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