Linear Algorithms for Control of Geometrical Allocation of Agents in Multi-Agent Systems

Simple and effective linear local algorithms for agents movement and allocation on a line and on a circle are proposed. It is based on the following assumptions: 1) the total number of agents in the system is unknown; 2) the future position of each agent is defined by its own coordinates and coordinates of its closest neighbors; 3) one or both of boundary agents may be fixed or movable. Stability and convergence for developed systems are proven and a number of examples demonstrate the work of the proposed algorithms.