Continuous-Time Q-Learning for Infinite-Horizon Discounted Cost Linear Quadratic Regulator Problems

This paper presents a method of Q-learning to solve the discounted linear quadratic regulator (LQR) problem for continuous-time (CT) continuous-state systems. Most available methods in the existing literature for CT systems to solve the LQR problem generally need partial or complete knowledge of the...

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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 45; no. 2; pp. 165 - 176
Main Authors: Palanisamy, Muthukumar, Modares, Hamidreza, Lewis, Frank L., Aurangzeb, Muhammad
Format: Journal Article
Language:English
Published: United States IEEE 01.02.2015
Subjects:
Approximate dynamic programming (ADP)
Approximation algorithms
continuous-time dynamical systems
Convergence
Discrete-time systems
Equations
Heuristic algorithms
infinite-horizon discounted cost function
integral reinforcement learning (IRL)
Mathematical model
Optimal control
Q-learning
value iteration (VI)
infinite-horizon discounted cost function
integral reinforcement learning (IRL)
Q-learning
continuous-time dynamical systems
value iteration (VI)
Approximate dynamic programming (ADP)
optimal control
ISSN:2168-2267, 2168-2275, 2168-2275
Online Access:Get full text
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Summary:This paper presents a method of Q-learning to solve the discounted linear quadratic regulator (LQR) problem for continuous-time (CT) continuous-state systems. Most available methods in the existing literature for CT systems to solve the LQR problem generally need partial or complete knowledge of the system dynamics. Q-learning is effective for unknown dynamical systems, but has generally been well understood only for discrete-time systems. The contribution of this paper is to present a Q-learning methodology for CT systems which solves the LQR problem without having any knowledge of the system dynamics. A natural and rigorous justified parameterization of the Q-function is given in terms of the state, the control input, and its derivatives. This parameterization allows the implementation of an online Q-learning algorithm for CT systems. The simulation results supporting the theoretical development are also presented.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2014.2322116