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. They are 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 end agents may be fixed or movable. Stability and convergence for developed systems are proven and a number of examples are given to demonstrate the work of the proposed algorithms.