  This paper investigates the problem of cooperative tuning of multi-agent
optimal control systems, where a network of agents (i.e. multiple coupled
optimal control systems) adjusts parameters in their dynamics, objective
functions, or controllers in a coordinated way to minimize the sum of their
loss functions. Different from classical techniques for tuning parameters in a
controller, we allow tunable parameters appearing in both the system dynamics
and the objective functions of each agent. A framework is developed to allow
all agents to reach a consensus on the tunable parameter, which minimizes team
loss. The key idea of the proposed algorithm rests on the integration of
consensus-based distributed optimization for a multi-agent system and a
gradient generator capturing the optimal performance as a function of the
parameter in the feedback loop tuning the parameter for each agent. Both
theoretical results and simulations for a synchronous multi-agent rendezvous
problem are provided to validate the proposed method for cooperative tuning of
multi-agent optimal control.
