This paper presents a robust optimal control algorithm for a Renewable Energy Management System (REMS) in a smart house grid having integrated solar energy and storage. The proposed method integrates \(H_{\infty }\) control theory with the Q-learning algorithm to develop a performance index function that minimizes the cost function, extends battery lifespan, rejects system disturbances, and balances grid pay-load effectively. This performance index is estimated to be using an evolving neural model, optimized through the Neuro-Evolution of Augmenting Topologies (NEAT) technique, while two 2-layer perceptron (2-LP) NNs are used to approximate the control law and the disturbance compensation law. The proposed approach ensures the convergence of the Q-learning function, control law, and disturbance compensation law to near-optimal values. To comprehensively validate the effectiveness and superiority of the algorithm, a numerical test is conducted using practically measured data, including electricity prices, load demand, and solar energy generation.
