Weights' Assignment in Multi-Agent Systems Under a Time-Varying Topology

The main objective of this paper is to design an optimal solution for weights' assignment in formation and reconfiguration control among a group of robots. The optimal solution must keep the control effort given to the whole system at its minimum possible level and guarantees that the desired configuration can be reached. In particular, the case of a single leader under a time-varying topology is considered. In contrast to the existing literature on this topic, we assume that the graph is weighted and time-varying; moreover, weights can be assigned freely. Under this setup, there are plenty of possible weights. However, determining a set of the best weights remains as an open problem because the control effort given to the agents must be minimized meanwhile the final desired states must be assured. In this paper, the problem of weights' assignment is discussed and formulated using the optimal control theory. The optimal control strategy is designed based on minimization of an index function and a solution is found using Hamiltton-Jacobi-Bellman equations. Finally, some simulation results are presented to illustrate the approach.