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This paper presents a state estimation-based robust optimal control strategy for influenza epidemics in an interactive human society in the presence of modeling uncertainties. Interactive society is influenced by the random entrance of individuals from other human societies whose effects can be modeled as a non-Gaussian noise. Since only the number of exposed and infected humans can be measured, states of the influenza epidemics are first estimated by an extended maximum correntropy Kalman filter (EMCKF) to provide a robust state estimation in the presence of the non-Gaussian noise. An online quadratic program (QP) optimization is then synthesized subject to a robust control Lyapunov function (RCLF) to minimize susceptible and infected humans, while minimizing and bounding the rates of vaccination and antiviral treatment. The joint QP-RCLF-EMCKF meets multiple design specifications such as state estimation, tracking, pointwise control optimality, and robustness to parameter uncertainty and state estimation errors that have not been achieved simultaneously in previous studies. The uniform ultimate boundedness (UUB)/convergence of error trajectories is guaranteed using a Lyapunov stability argument. The soundness of the proposed approach is validated on the influenza epidemics of an interactive human society with a population of 16000. Simulation results show that the QP-RCLF-EMCKF achieves appropriate tracking and state estimation performance. The robustness of the proposed controller is finally illustrated in the presence of modeling error and non-Gaussian noise.