Partially asynchronous distributed algorithms for 2-dimensional multi-agent supporting systems

This paper studies a physical surface whose shape is controlled by a multi-agent supporting system (MASS) consisting of components that cooperate to restore the original shape of the surface after an arbitrary disturbance. Synchronous distributed algorithms for 2-dimensional MASS have been investigated in the literature. This paper considers two models for 2-dimensional MASS having different number of interconnections (4 and 8). Two partially asynchronous algorithms corresponding to the two topologies are proposed and proven to be convergent, if the vertical disturbances vary sufficiently slower than the convergence time of the system. The adjacent error becomes zero when the system converges. Finally simulation results for the two models of 2-dimensional MASS are shown to confirm the theoretical findings.