Negotiation between dynamical systems with connectivity constraints

Multi-agent systems (MAS) have been an important area of study over the past few years. In this work we consider a MAS where a team of agents must coordinate to reach an agreement on their state in finite-time, while simultaneously attempting to minimize their own cost functions. Agents cooperate with each other by means of communication, and thus an additional requirement is the agents maintain their communication network during their trajectories - this leads to a constraint on the distances between neighbouring agents. We propose a real time sub-optimal solution for this agreement problem. The algorithm is based on the well-known dual sub-gradient algorithm for solving distributed optimization problems. To ensure the algorithm does not violate the distance connectivity constraints between neighbouring agents, we propose a modification to the sub-gradient algorithm that projects the Lagrange multipliers associated with the distance constraints onto a bounded set that ensures the distance between neighbouring agents remains within the prescribed limits. The main contribution for this work is an algorithm that solves the problem for the 2-agent case. We demonstrate the result using numerical simulations.