Active Synchronization for Double-Integrator Network Systems Without Velocity Information

Abstract

Of particular interest in this paper is to study the active synchronization (act-synchronization) problem for double-integrator network systems without velocity information. To this end, scaling parameters are suggested to quantify the degree of act-synchronization for different agents. And weighted gains are employed to assure that there is a simple zero eigenvalue with the other ones sharing positive real parts. An auxiliary variable is introduced to mitigate the unavailability on velocity information. Thus only the directed spanning tree requirement in the content of algebraic graph theory is required. This exhibits a clear distinction from signed-graph or scaled consensus as non-unitary signs for scaling parameter and weighted gain are allowed. It is shown that the condition for act-synchronization is related to weighted gain, scaling parameter, the real and imaginary parts of the involved eigenvalues. With the constraint on identical weighted gain and scaling parameter for position and auxiliary variables, it is proven that act-synchronization can be exponentially guaranteed using the Lyapunov-based technique. Finally, the multiple unmanned ground vehicles system and the 10-generator in IEEE 39-bus system are given to facilitate the proposed configuration and the theoretical findings.