  Passivity-based approaches have been suggested as a solution to the problem
of decentralised control design in many multi-agent network control problems
due to the plug- and-play functionality they provide. However, it is not clear
if these controllers are optimal at a network level due to their inherently
local formulation, with designers often relying on heuristics to achieve
desired global performance. On the other hand, solving for an optimal
controller is not guaranteed to produce a passive system. In this paper, we
address these dual problems by using inverse optimal control theory to
formulate a set of sufficient local conditions, which when satisfied ensure
that the resulting decentralised control policies are the solution to a network
optimal control problem, while at the same time satisfying appropriate
passivity properties. These conditions are then reformulated into a set of
linear matrix inequalities (LMIs) which can be used to yield such controllers
for linear systems. The proposed approach is demonstrated through a DC
microgrid case study. The results substantiate the feasibility and efficacy of
the presented method.
