A theoretical study of different leader roles in networks

• Published in: IEEE transactions on automatic control Vol. 51; no. 7; pp. 1156 - 1161
• Main Authors: Wei Wang, Slotine, J.-J.E.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation; Adaptative systems; Aggregates; Animals; Applied sciences; Artificial intelligence; Biology; Computer science; control theory; systems; Connectionism. Neural networks; Control theory. Systems; Diseases; Dynamic tests; Dynamics; Evolution (biology); Evolutionary; Exact sciences and technology; Frequency synchronization; group cooperation; Intelligent networks; Knowledge base; leaders; Local oscillators; Modelling and identification; Networks; Neural networks; Nonlinear systems; Oscillators; Pacemakers; Synchronization; System theory; group cooperation; Evolutionary algorithm; Biological model; Lyapunov method; Collective process; Biology; leaders; Dynamical system; Synchronization; networks; Modeling; Dynamic conditions; Global local method; Analog; Cooperation; Optimal trajectory; Network; Adaptation
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2006.878754

We study synchronization conditions for distributed dynamic networks with different types of leaders. The role of a "power" leader specifying a desired global state trajectory through local interactions has long been recognized and modeled. This note introduces the complementary notion of a "knowledge" leader holding information on the target dynamics, which is propagated to the entire network through local adaptation mechanisms. Different types of leaders can coexist in the same network. For instance, in a network of locally connected oscillators, the power leader may set the global phase while the knowledge leader may set the global frequency and the global amplitude. Knowledge-based leader-followers networks have many analogs in biology, e.g., in evolutionary processes and disease propagation.