This work is concerned with a class of hybrid LQG (linear quadratic Gaussian)
regulator problems modulated by continuous-time Markov chains. In contrast to
the traditional LQG models, the systems have both continuous dynamics and
discrete events. In lieu of a model with constant coefficients, these coefficients
vary with time and exhibit piecewise constant behavior. At any time t, the system
follows a stochastic differential equation in which the coefficients take one of the
m
possible configurations where m
is usually large. The system may jump to any
of the possible configurations at random times. Further, the control weight in the
cost functional is allowed to be indefinite. To reduce the complexity, the Markov
chain is formulated as singularly perturbed with a small parameter. Our effort is
devoted to solving the limit problem when the small parameter tends to zero via
the framework of weak convergence. Although the limit system is still modulated
by a Markov chain, it has a much smaller state space and thus, much reduced
complexity.
