  Although the mean-variance control was initially formulated for financial
portfolio management problems in which one wants to maximize expected return
and control the risk, our motivations also stem from highway vehicle platoon
controls that aim to maximize highway utility while ensuring zero accident.
This paper develops near-optimal mean-variance controls of switching diffusion
systems. To reduce the computational complexity, with motivations from earlier
work on singularly perturbed Markovian systems \cite{SethiZ94,Yin&Zhang,GZB},
we use a two-time-scale formulation to treat the underlying systems, which is
represented by use of a small parameter. As the small parameter goes to 0, we
obtain a limit problem. Using the limit problem as a guide, we construct
controls for the original problem, and show that the control so constructed is
nearly optimal.
