Large deviations for systems driven by two-time-scale nonhomogeneous Markovian chains and applications to optimal control problems

This paper is based on our paper [15]. We present the main results; the verbatim proofs are omitted due to the page limitation. We develop large deviations principles for systems driven by continuous-time Markov chains with two-time scales and related optimal control problems. A distinct feature of our setup is that the Markov chain under consideration is time dependent or inhomogeneous. The use of two-time-scale formulation stems from the effort of reducing computational complexity in a wide variety of applications in control, optimization, and systems theory. Then the results are applied to certain dynamic systems and LQ control problems.