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