Continuous-time reinforcement learning for linear-quadratic tracking problem using policy iteration method

Recieved: 10/31/2025

Accepted: 12/31/2025

Keywords: reinforcement learning, linear-quadratic tracking, policy iteration, Riccati equation, Lyapunov equation

Available in the on-line version with: 24.07.2026

To cite this article

Melnikov N.B., Smovzh I.N. Continuous-time reinforcement learning for linear-quadratic tracking problem using policy iteration method. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2026. N 2, p.61-70 https://doi.org/10.55959/MSU/0137–0782–15–2026–50–2–61–70.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Melnikov N.B. (Lomonosov Moscow State University (MSU))
Smovzh I.N. (Lomonosov Moscow State University (MSU))

Abstract

For a linear-quadratic tracking problem with a target trajectory described by a linear dynamics, convergence of reinforcement learning using policy iteration method is investigated. A proof of convergence is given, and convergence rate is analyzed. Namely, it is proven that the policy iteration method converges and has a quadratic convergence rate under relaxed constraints on the initial control.