Control via Leadership of Opinion Dynamics with State and Time-Dependent Interactions

We study opinion dynamics systems controlled by a leader. Following findings from experimental social psychology, the influence weights considered here have the peculiarity to be both state and time dependent. This allows for instance to model loss of patience or interest of individuals. The opinion of the leader is assumed to be controlled using a saturated control. The objective of the leader is to make all agents agree on a desired consensus value. First, all agents are gathered around the leader, which then steers all agents toward the target consensus value, where consensus is achieved. Trajectory tracking is also investigated. The time-dependent interactions have a significant impact on the control law. To achieve the control, the time-dependent term in the interactions is assumed to be persistent in time. Our results are illustrated by numerical simulation throughout the paper.

[1]  Carl I. Hovland,et al.  Reconciling conflicting results derived from experimental and survey studies of attitude change. , 1959 .

[2]  John N. Tsitsiklis,et al.  On Krause's Multi-Agent Consensus Model With State-Dependent Connectivity , 2008, IEEE Transactions on Automatic Control.

[3]  Christoph Niemann,et al.  Optimal Opinion Control: The Campaign Problem , 2015, Journal of Artificial Societies and Social Simulation.

[4]  Marc Jungers,et al.  Transient cluster formation in generalized Hegselmann-Krause opinion dynamics , 2016, 2016 European Control Conference (ECC).

[5]  Samuel Martin,et al.  Opinion dynamics control by leadership with bounded influence , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[6]  Benedetto Piccoli,et al.  Sparse feedback stabilization of multi-agent dynamics , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[7]  Basel Alomair,et al.  Leader selection in multi-agent systems for smooth convergence via fast mixing , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[8]  Chiara Ravazzi,et al.  Ergodic Randomized Algorithms and Dynamics Over Networks , 2013, IEEE Transactions on Control of Network Systems.

[9]  A. Cohen,et al.  Communication discrepancy and attitude change: A dissonance theory approach1 , 1959 .

[10]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[11]  Francesco Bullo,et al.  Controllability Metrics, Limitations and Algorithms for Complex Networks , 2013, IEEE Transactions on Control of Network Systems.

[12]  Jan Lorenz,et al.  Continuous Opinion Dynamics under Bounded Confidence: A Survey , 2007, 0707.1762.

[13]  Antoine Girard,et al.  Continuous-Time Consensus under Persistent Connectivity and Slow Divergence of Reciprocal Interaction Weights , 2013, SIAM J. Control. Optim..

[14]  Daisuke Nakanishi,et al.  Majority Influence Process in Group Judgment: Test of the Social Judgment Scheme Model in a Group Polarization Context , 2002 .

[15]  T. H. Gronwall.  Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential Equations , 1919 .

[16]  Asuman E. Ozdaglar,et al.  Opinion Fluctuations and Disagreement in Social Networks , 2010, Math. Oper. Res..

[17]  O. J. Harvey,et al.  Assimilation and contrast effects in reactions to communication and attitude change. , 1957, Journal of abnormal psychology.

[18]  Vincent D. Blondel,et al.  Modelling Influence and Opinion Evolution in Online Collective Behaviour , 2015, PloS one.

[19]  Noah E. Friedkin,et al.  Social influence and opinions , 1990 .

[20]  Antoine Girard,et al.  Opinion Dynamics With Decaying Confidence: Application to Community Detection in Graphs , 2009, IEEE Transactions on Automatic Control.

[21]  John N. Tsitsiklis,et al.  Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications , 2009, SIAM J. Control. Optim..

[22]  Albert-László Barabási,et al.  Control Centrality and Hierarchical Structure in Complex Networks , 2012, PloS one.

[23]  M. Degroot.  Reaching a Consensus , 1974 .

[24]  Sascha Kurz,et al.  Optimal control of the freezing time in the Hegselmann–Krause dynamics , 2014, ArXiv.

[25]  Elliot Aronson,et al.  Communicator credibility and communication discrepancy as determinants of opinion change. , 1963 .

[26]  J. H. Davis,et al.  Group decision making and quantitative judgments: A consensus model. , 1996 .

[27]  Alfio Borzì,et al.  On the control through leadership of the Hegselmann–Krause opinion formation model , 2015 .

[28]  Samuel Martin,et al.  Continuous-Time Consensus Under Non-Instantaneous Reciprocity , 2014, IEEE Transactions on Automatic Control.

[29]  P. Rauschnabel,et al.  Elements of strategic social media marketing: A holistic framework , 2017 .

[30]  Roberto Tempo,et al.  A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part II , 2018, Annu. Rev. Control..

[31]  R. Srikant,et al.  Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate , 2014, Autom..