Finite-time optimal feedback control mechanism for knowledge transmission in complex networks via model predictive control

In this paper, the finite-time (FT) optimal feedback control problems of knowledge transmission processes in complex networks via model predictive control (MPC) have been studied. Firstly, we build a knowledge transmission Susceptible-Infected-Hesitation (SIH) model in complex networks. Secondly, interventional control strategies are designed to regulate the system parameters to improve the performance of knowledge dissemination, including improving self-learning ability, acquaintance influence, and review rate. With the help of the Lyapunov-based HJB optimal control method, the existence of the optimal solution to the economic optimal problem of the knowledge transmission control model is guaranteed. Then, the optimal control solution is derived by using Pontryagin's maximum principle. To focus on the performance indicators and state trajectories of the system and enable the controller to modify in real-time according to the state in a fixed time interval as soon as possible, an MPC based on FT feedback is proposed for the first time. Furthermore, under feedback control and initial conditions, the control knowledge dissemination model is FT stable. Numerical simulations are provided to verify the proposed method.