A Hierarchical Optimal Control of Uncertain and Time-Varying Knowledge Dissemination Model in Complex Network

Abstract

In this paper, considering the multifactor influence of the knowledge dissemination process, a new ignorant-knower-spreader-forgetter (IKSF) knowledge dissemination model is proposed, which considers internalization mechanism, degradation mechanism, communication, and willingness, as well as time-varying and uncertain parameters. First, we prove that the knowledge loss equilibrium of the model is globally asymptotically stable when the basic reproduction number $R_0<1$ , and knowledge is permanent when $R_0>1$ . Next, improving the willingness of knower individuals and reducing the knowledge degradation function of spreader individuals can make the best effect of propagation; a hierarchical control strategy is designed. At the upper layer, an effective optimal control mechanism of the IKSF knowledge dissemination model is studied to provide optimal control action and minimization costs. At the lower layer, to guarantee robustness control performance and track the control targets, an intervention optimal guaranteed cost control strategy for the IKSF knowledge dissemination system with uncertain parameters is studied. Converting the controller’s design problem into a minimization problem with linear matrix inequalities, not only the impact of uncertain parameters is reduced but also the propagation effect of the knowledge dissemination model is guaranteed. Simulation results confirm our method.