Abstract
In this paper, we propose a novel Q-learning method based on multirate generalized policy iteration (MGPI) for unknown discrete-time (DT) linear quadratic regulation (LQR) problems. Q-learning is an effective scheme for unknown dynamical systems because it does not require any knowledge of the system dynamics to solve optimal control problems. By applying the MGPI concept, which is an extension of basic GPI with multirate time horizon steps, a new Q-learning algorithm is proposed for solving the LQR problem. Further, it is proven that the proposed algorithm converges to an optimal solution i.e., it learns the optimal control policy iteratively using the states and the control-input information. Finally, we employ the two degree-of-freedom helicopter model to verify the effectiveness of the proposed method and investigate its convergence properties.
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