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*also affiliated with University Paris-Saclay

We study the impulse control of a general Markov-Feller process in a compact metric space E with a long term average (or ergodic) cost when the impulse instants are restricted to be the arrival times of an exogenous signal process; this restriction is referred to as a constraint. The admissible impulses values belong to a compact subset Γ(x) of E depending on the state x. A characterization of the optimal cost is obtained as solution of a HJB equation using an auxiliary ergodic control problem in discrete time, and an optimal impulse control is identified. Some extensions are discussed. This talk is based on a joint work with JL Menaldi.