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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/1806.00052 |
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| _version_ | 1866917683749978112 |
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| author | Avila, Daniel Junca, Mauricio |
| author_facet | Avila, Daniel Junca, Mauricio |
| contents | 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 problems. Finally, we apply our results to a example of an object that navigates under stochastic influence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_00052 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On reachability of Markov chains: A long-run average approach Avila, Daniel Junca, Mauricio Optimization and Control 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 problems. Finally, we apply our results to a example of an object that navigates under stochastic influence. |
| title | On reachability of Markov chains: A long-run average approach |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/1806.00052 |