  Motivated by applications arising in networked systems, this work examines
controlled regime-switching systems that stem from a mean-variance formulation.
A main point is that the switching process is a hidden Markov chain. An
additional piece of information, namely, a noisy observation of switching
process corrupted by white noise is available. We focus on minimizing the
variance subject to a fixed terminal expectation. Using the Wonham filter, we
convert the partially observed system to a completely observable one first.
Since closed-form solutions are virtually impossible be obtained, a Markov
chain approximation method is used to devise a computational scheme.
Convergence of the algorithm is obtained. A numerical example is provided to
demonstrate the results.
