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In this paper we present the stability and convergence results for dynamic programming-based reinforcement learning applied to linear quadratic regulation (LQR). The specific algorithm we analyze is based on Q-learning and it is proven to converge to an optimal controller provided that the underlying system is controllable and a particular signal vector is persistently excited. This is the first convergence result for DP-based reinforcement learning algorithms for a continuous problem.
Bradtke et al. (Wed,) studied this question.
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