A Distributed Feedback-based Framework for Nonlinear Aggregative Optimal Control

In this paper, we propose a distributed, first-order, feedback-based approach to solve nonlinear optimal control problems with aggregative cost functions over networks of cooperative multi-agent systems. Taking inspiration from a centralized, first-order optimal control framework, named GoPRONTO, we propose a distributed method exploiting a feedback scheme iteratively updated according to a distributed tracking mechanism. Due to the aggregative structure of the problem and the desired distributed paradigm, the centralized scheme would require global quantities that are not locally available. Thus, our distributed method concurrently updates a proxy of the centralized scheme with a set of local, auxiliary variables named trackers which suitably exploit inter-agent communication to reconstruct the global quantities. By relying on LaSalle-based arguments, we theoretically prove that our algorithm generates a sequence of trajectories converging to the set of trajectories satisfying the first-order necessary conditions for optimality. Finally, we corroborate the theoretical results with numerical simulations on a distributed optimal control application for a fleet of 50 quadrotors.