Finite-time consensus for controlled dynamical systems in network

ABSTRACTThe key challenges in networked dynamical systems are the component heterogeneities, nonlinearities, and the high dimension of the formulated vector of state variables. In this paper, the emphasise is put on two classes of systems in network include most controlled driftless systems as well as systems with drift. For each model structure that defines homogeneous and heterogeneous multi-system behaviour, we derive protocols leading to finite-time consensus. For each model evolving in networks forming a homogeneous or heterogeneous multi-system, protocols integrating sufficient conditions are derived leading to finite-time consensus. Likewise, for the networking topology, we make use of fixed directed and undirected graphs. To prove our approaches, finite-time stability theory and Lyapunov methods are considered. As illustrative examples, the homogeneous multi-unicycle kinematics and the homogeneous/heterogeneous multi-second order dynamics in networks are studied.