Inverse Optimal Control and Passivity-Based Design for Converter-Based Microgrids

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 solved to obtain 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.