LARGE DEVIATIONS FOR TWO-TIME-SCALE SYSTEMS DRIVEN BY NONHOMOGENEOUS MARKOV CHAINS AND ASSOCIATED OPTIMAL CONTROL PROBLEMS

This work develops 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 formulations stems from the effort of reducing computational complexity in a wide variety of applications in control, optimization, and systems theory. Starting with a rapidly fluctuating Markovian system, under irreducibility conditions, both large deviations upper and lower bounds are established for systems with a fixed terminal time and for time-varying dynamic systems. Then the results are applied to certain dynamic systems and linear quadratic control problems.