State estimation-based robust optimal control of influenza epidemics in an interactive human society

Abstract

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 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, the 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 main contribution of this work is twofold. First, the joint QP-RCLF-EMCKF strategy 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. Second, the uniform ultimate boundedness (UUB)/convergence of all error trajectories is guaranteed by using a Lyapunov stability argument. Simulation results show that the proposed approach achieves appropriate tracking and state estimation performance with good robustness.