Stabilization of stochastic systems with hidden Markovian jumps

This paper considers the adaptive control of discrete-time hybrid stochastic systems with unknown randomly jumping parameters described by a finite-state hidden Markov chain. An intuitive yet longstanding conjecture in this area is that such hybrid systems can be adaptively stabilized whenever the rate of transition of the hidden Markov chain is small enough. This paper provides a rigorous positive answer to this conjecture by establishing the global stability of a gradient-algorithm-based adaptive linear-quadratic control.