In this paper, we propose an efficient algorithm to find an optimal control policy in a discrete-time hidden mode stochastic hybrid system, which is a special case of partially observable discrete-time stochastic hybrid systems in which only discrete states are hidden. Many human-centered systems can be modeled as such systems, in which the intent of the human operator is unknown and can be modeled as the hidden mode. In the literature, the optimal control problem of hidden mode stochastic hybrid system is known to have high computational complexity due to the continuous state space. In this paper, we will tackle this computational challenge by using local quadratic functions to approximate the optimal expected reward, which does not have a closed-form expression in general. We will show the efficacy of our proposed method, and the significant improvement in the computational time.
