On nearly optimal controls of hybrid LQG problems

The paper is concerned with hybrid control of a class of linear quadratic Gaussian (LQG) systems modulated by a finite-state Markov chain. It develops approximation schemes for systems involving singularly perturbed Markov chains with weak and strong interactions, which are useful for natural time-scale separation and for large-scale Markovian systems. The presentation encompasses three cases: the recurrent Markov chains, inclusion of transient states, and inclusion of absorbing states. Near optimality of the approximation schemes is obtained, and a numerical example is presented. Computational results indicate our approximation schemes perform well.