Optimal filtering and control of network information epidemics

In this article, we propose an optimal control scheme for information epidemics with stochastic uncertainties aiming at maximizing information diffusion and minimizing the control consumption. The information epidemic dynamics is represented by a network Susceptible-Infected-Susceptible (SIS) model contaminated by both process and observation noises to describe a perturbed disease-like information diffusion process. To reconstruct the contaminated system states, we design an optimal filter which ensures minimized estimation errors in a quadratic sense. The state estimation is then utilized to develop the optimal controller, for which the optimality of the closed-loop system is guaranteed by a separation principle. The designed optimal filter and controller, together with the separation principle, form a complete solution for the optimal control of network information epidemics with stochastic perturbations. Such optimal-filtering-based control strategy is also generalizable to a wider range of networked nonlinear systems. In the numerical experiments on real network data, the effectiveness of the proposed optimal control is validated and confirmed.