Abstract
This paper deals with an opinion formation model, that obeys a nonlinear system of fractional-order differential equations. We introduce a virtual leader in order to attain a consensus. Sufficient conditions are established to ensure that the opinions of all agents globally asymptotically approach the opinion of the leader. We also address the problem of designing optimal control strategies for the leader so that the followers tend to consensus in the most efficient way. A variational integrator scheme is applied to solve the leader–follower optimal control problem. Finally, in order to verify the theoretical analysis, several particular examples are presented.
Highlights
The process of opinion formation in a social network is rapidly attracting the attention of scholars in many disciplines, Journal of Optimization Theory and Applications (2019) 182:1171–1185 ranging from sociology to mathematics [1,2,3,4,5,6]
We use the idea of variational integrators, which consists of two steps: first, we define a discrete version of problem (11)–(12); second, we apply the corresponding discrete Weak Pontryagin’s Maximum Principle to it
The agent-based model of opinion formation given by the system of nonlinear fractional differential equations was investigated
Summary
The process of opinion formation in a social network (a network of social actors connected by social ties) is rapidly attracting the attention of scholars in many disciplines,. Consensus is a behavior, that we would expect in opinion formation models, there are situations when the opinions do not reach consensus and we observe polarization of opinions or chaos [12,13,14] In such situations, one possible way to steer all agents to reach a consensus consists in introducing a (virtual) leader to the system and possibly controlling the leader [15,16,17,18]. We study a nonlinear fractional leader–follower model of opinion formation. We address the problem of designing optimal control strategies for the leader so that the followers tend to consensus in the most efficient way. The fractional opinion formation model with a leader is discussed in Sect.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
