Abstract
This paper mathematically analyzes the integral generalized policy iteration (I-GPI) algorithms applied to a class of continuous-time linear quadratic regulation (LQR) problems with the unknown system matrix A. GPI is the general idea of interacting policy evaluation and policy improvement steps of policy iteration (PI), for computing the optimal policy. We first introduce the update horizon H, and then show that (i) all of the I-GPI methods with the same H can be considered equivalent and that (ii) the value function approximated in the policy evaluation step monotonically converges to the exact one as H→∞. This reveals the relation between the computational complexity and the update (or time) horizon of I-GPI as well as between I-PI and I-GPI in the limit H→∞. We also provide and discuss two modes of convergence of I-GPI; I-GPI behaves like PI in one mode, and in the other mode, it performs like value iteration for discrete-time LQR and infinitesimal GPI (H→0). From these results, a new classification of the integral reinforcement learning is formed with respect to H. Two matrix inequality conditions for stability, the region of local monotone convergence, and data-driven (adaptive) implementation methods are also provided with detailed discussion. Numerical simulations are carried out for verification and further investigations.
| Original language | English |
|---|---|
| Pages (from-to) | 475-489 |
| Number of pages | 15 |
| Journal | Automatica |
| Volume | 50 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2014 Feb 1 |
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All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Electrical and Electronic Engineering
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On integral generalized policy iteration for continuous-time linear quadratic regulations. / Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho.
In: Automatica, Vol. 50, No. 2, 01.02.2014, p. 475-489.Research output: Contribution to journal › Article
TY - JOUR
T1 - On integral generalized policy iteration for continuous-time linear quadratic regulations
AU - Lee, Jae Young
AU - Park, Jin Bae
AU - Choi, Yoon Ho
PY - 2014/2/1
Y1 - 2014/2/1
N2 - This paper mathematically analyzes the integral generalized policy iteration (I-GPI) algorithms applied to a class of continuous-time linear quadratic regulation (LQR) problems with the unknown system matrix A. GPI is the general idea of interacting policy evaluation and policy improvement steps of policy iteration (PI), for computing the optimal policy. We first introduce the update horizon H, and then show that (i) all of the I-GPI methods with the same H can be considered equivalent and that (ii) the value function approximated in the policy evaluation step monotonically converges to the exact one as H→∞. This reveals the relation between the computational complexity and the update (or time) horizon of I-GPI as well as between I-PI and I-GPI in the limit H→∞. We also provide and discuss two modes of convergence of I-GPI; I-GPI behaves like PI in one mode, and in the other mode, it performs like value iteration for discrete-time LQR and infinitesimal GPI (H→0). From these results, a new classification of the integral reinforcement learning is formed with respect to H. Two matrix inequality conditions for stability, the region of local monotone convergence, and data-driven (adaptive) implementation methods are also provided with detailed discussion. Numerical simulations are carried out for verification and further investigations.
AB - This paper mathematically analyzes the integral generalized policy iteration (I-GPI) algorithms applied to a class of continuous-time linear quadratic regulation (LQR) problems with the unknown system matrix A. GPI is the general idea of interacting policy evaluation and policy improvement steps of policy iteration (PI), for computing the optimal policy. We first introduce the update horizon H, and then show that (i) all of the I-GPI methods with the same H can be considered equivalent and that (ii) the value function approximated in the policy evaluation step monotonically converges to the exact one as H→∞. This reveals the relation between the computational complexity and the update (or time) horizon of I-GPI as well as between I-PI and I-GPI in the limit H→∞. We also provide and discuss two modes of convergence of I-GPI; I-GPI behaves like PI in one mode, and in the other mode, it performs like value iteration for discrete-time LQR and infinitesimal GPI (H→0). From these results, a new classification of the integral reinforcement learning is formed with respect to H. Two matrix inequality conditions for stability, the region of local monotone convergence, and data-driven (adaptive) implementation methods are also provided with detailed discussion. Numerical simulations are carried out for verification and further investigations.
UR - http://www.scopus.com/inward/record.url?scp=84893829511&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84893829511&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2013.12.009
DO - 10.1016/j.automatica.2013.12.009
M3 - Article
AN - SCOPUS:84893829511
VL - 50
SP - 475
EP - 489
JO - Automatica
JF - Automatica
SN - 0005-1098
IS - 2
ER -