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On reachability of Markov chains: A long-run average approach

Author

Listed:
  • Junca, M.
  • Ávila, D.

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

Abstract

We consider a Markov control model in discrete time with countable both state space and action space. Using the value function of a suitable long-run average reward problem, we study various reachability/controllability problems. First, we characterize the domain of attraction and escape set of the system, and a generalization called p-domain of attraction, using the aforementioned value function. Next, we solve the problem of maximizing the probability of reaching a set $A$ while avoiding a set B. Finally, we consider a constrained version of the previous problem where we ask for the probability of reaching the set $B$ to be bounded. In the finite case, we use linear programming formulations to solve these problem.

Suggested Citation

  • Junca, M. & Ávila, D., 2021. "On reachability of Markov chains: A long-run average approach," LIDAM Reprints CORE 3179, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3179
    DOI: https://doi.org/10.1109/tac.2021.3071334
    Note: In: IEEE Transactions on Automatic Control, 2021
    as

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