Conjectures on Adaptive Autonomous Synchronization of Heterogeneous Multi-Agent Systems

Recently, a new type of synchronization problem called autonomous synchronization was formulated where neither the synchronized agent dynamics nor the synchronized states are specified a priori. Through a dynamics update law together with the synchronizing control law, the heterogeneous multi-agent systems (MAS) synchronize with one another autonomously. In this paper, we propose a dynamics update scheme which can adaptively select the parameter in the dynamics update law without requiring the knowledge of the underlying communication graph or the eventual synchronized dynamics. In this way, we reduce the constraints of the design of autonomous synchronization controllers. Two conjectures are proposed on solvability of the adaptive autonomous synchronization problem in both continuous-time and discrete-time environments. Numerical simulations are provided to illustrate the solutions.