On the Trade-Off Between Communication and Execution Overhead for Control of Multi-Agent Systems

For multi-agent systems, it is common to encode the task as an optimization problem with two distinctly different solution methodologies - one is to directly apply control inputs as optimization updates, the other is to solve the optimization problem through communications before applying actual control inputs. This reveals an important trade-off between communication and execution overhead for control of multiagent systems. To formally study this trade-off, we restrict our consideration to a class of commonly studied multi-agent problems where the objective function is the sum of a set of edge potential functions. The gradient descent algorithm and Newton's method are viewed as the proxy for the pure execution and the pure communication strategy, respectively. We propose an algorithm based on truncated Newton's method that provides tunable levels of trade-off between communication and execution efforts. Theoretical results on the convergence rate of the purposed algorithm are studied for the consensus problem under different trade-off strategies. The performance of the proposed algorithm is validated through simulation.