Containment control for a social network with state-dependent connectivity

• Zhen Kan ^[1] ; Justin R. Klotz ^[1] ; Eduardo L. Pasiliao, Jr ^[2] ; Warren E. Dixon ^[1]
  1. [1] University of Florida

     University of Florida

     Estados Unidos

     
  2. [2] Air Force Research Laboratory

     Air Force Research Laboratory

     City of Dayton, Estados Unidos

     
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 56, 2015, págs. 86-92
• Idioma: inglés
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• Resumen

  • Social interactions influence our thoughts, opinions and actions. In this paper, social interactions are studied within a group of individuals composed of influential social leaders and followers. Each person is assumed to maintain a social state, which can be an emotional state or an opinion. Followers update their social states based on the states of local neighbors, while social leaders maintain a constant desired state. Social interactions are modeled as a general directed graph where each directed edge represents an influence from one person to another. Motivated by the non-local property of fractional-order systems, the social response of individuals in the network are modeled by fractional-order dynamics whose states depend on influences from local neighbors and past experiences. A decentralized influence method is then developed to maintain existing social influence between individuals (i.e., without isolating peers in the group) and to influence the social group to a common desired state (i.e., within a convex hull spanned by social leaders). Mittag-Leffler stability methods are used to prove the asymptotic convergence of the networked fractional-order system.