Gradual-impulsive control for continuous-time Markov decision processes with total undiscounted costs and constraints: linear programming approach via a reduction method

We consider the constrained optimal control problem for a continuous-time Markov decision process (CTMDP) with gradual-impulsive control. The performance criteria are the expected total undiscounted costs (from the running cost and the impulsive cost). We justify fully a reduction method, and close an open issue in the previous literature. The reduction method induces an equivalent but simpler standard CTMDP model with gradual control only, based on which, we establish effectively, under rather natural conditions, a linear programming approach for solving the concerned constrained optimal control problem.