This paper studies the impulse control of a general Markov process under the average (or ergodic) cost when the impulse instants are restricted to be the arrival times of an exogenous process, and this restriction is referred to as a constraint. A detailed setting is described, a characterization of the optimal cost is obtained as a solution of an HJB equation, and an optimal impulse control is identified.
Control Theory | Other Applied Mathematics
J. L. Menaldi and M. Robin, On Some Ergodic Impulse Control Problems with Constraint, SIAM J. Control Optim., 56 (2018), pp. 2690-2711. doi: 10.1137/17M1147573