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In this paper, we investigate team optimal control of coupled major-minorsubsystems with mean-field sharing. In such a model, there is one majorsubsystem that directly influences the dynamics of $n$ homogeneous minorsubsystems; however, the minor subsystems influence the dynamics of the majorsubsystem and each other only through their mean behaviour (indirectly). Inthis model, the major and the minor subsystems are arbitrarily coupled in thecost and have mean-field sharing information structure. We propose a two-stepapproach. In the first step, we describe a mean-field sharing model withmultiple types of minor subsystems as a generalization of the mean-fieldsharing model of Arabneydi and Mahajan, CDC 2014. In the second step, we usethe results obtained in the first step to construct a dynamic programmingdecomposition to identify optimal strategies for the major and the minorsubsystems. We present an example with numerical results to illustrate theapproach.

Team Optimal Control of Coupled Major-Minor Subsystems with Mean-Field Sharing