In this paper, an integral reinforcement learning (IRL) algorithm on an actor-critic structure is developed to learn online the solution to the Hamilton-Jacobi-Bellman equation for partially-unknown constrained-input systems. The technique of experience replay is used to update the critic weights to solve an IRL Bellman equation. This means, unlike existing reinforcement learning algorithms, recorded past experiences are used concurrently with current data for adaptation of the critic weights. It is shown that using this technique, instead of the traditional persistence of excitation condition which is often difficult or impossible to verify online, an easy-to-check condition on the richness of the recorded data is sufficient to guarantee convergence to a near-optimal control law. Stability of the proposed feedback control law is shown and the effectiveness of the proposed method is illustrated with simulation examples. (C) 2013 Elsevier Ltd. All rights reserved.