On interconnected multi-agent dynamical systems with non-uniform heterogeneous coupling link weights

Abstract

With the increase of terrorism, the ability for law enforcement and government agencies to make intelligent decisions on the fly has become critical. When under attack, it is of utter importance to make timely decisions early enough for the information to reach its destination in time. But how one can know the maximum time by which a decision ought to be made? While little work and still in its infancy has been reported in the literature to address this problem, more work, however, has been done on the controllability and observability of interconnected systems. The approach we take in this paper to address this problem is to study the stability (convergence time) of an interconnected dynamical system (IDS) with respect to its connectivity. We select a class of IDSs as a case study in our analysis. In particular, we show that for the class of IDSs selected the more connected the dynamical systems are, the longer it will take for the overall system to stabilize. We propose a way to analytically derive the convergence time of the system based on its varying interconnections. Finally, the applications of what is proposed is not subject to this problem only, but also to robots/ground/flying vehicles/ formation, neural networks, and any other field where a network of dynamical systems is employed.