Achieving consensus amongst self-propelling agents by enforcing sliding modes

An algorithm, based on sliding mode control and graph algebraic theories, for the provision of consensus to a swarm of self-propelling agents is presented. Swarms, comprised of agents with first-order dynamics, that can be described by fully-connected and connected graphs with time-invariant topologies are considered. For consensus, the agents´ inputs are designed to enforce sliding mode on surfaces that depend on the graph Laplacian matrix. The property of sliding mode occurring within a finite time interval, which can be varied, is lent to the swarm and it is this facet that distinguishes the proposed algorithm. As will be shown, applying this algorithm results the swarm achieving a constant consensus value equal to the average of the largest and smallest initial states of the agents. Owing to this result, by introducing a virtual agent with a pre-calculated initial condition, the algorithm allows for the tuning of the consensus value.