Efficient Strategy Synthesis for MDPs with Resource Constraints

Frantisek Blahoudek, Petr Novotny, Melkior Ornik, Pranay Thangeda, Ufuk Topcu

Research output: Contribution to journalArticlepeer-review


We consider qualitative strategy synthesis for the formalism called consumption Markov decision processes. This formalism can model the dynamics of an agent that operates under resource constraints in a stochastic environment. The presented algorithms work in time polynomial with respect to the representation of the model and they synthesize strategies ensuring that a given set of goal states will be reached (once or infinitely many times) with probability 1 without resource exhaustion. In particular, when the amount of resource becomes too low to safely continue in the mission, the strategy changes course of the agent toward one of a designated set of reload states where the agent replenishes the resource to full capacity; with a sufficient amount of resource, the agent attempts to fulfill the mission again. We also present two heuristics that attempt to reduce the expected time that the agent needs to fulfill the given mission, a parameter important in practical planning. The presented algorithms were implemented, and the numerical examples demonstrate the effectiveness (in terms of computation time) of the planning approach based on consumption Markov decision processes and the positive impact of the two heuristics on planning in a realistic example.

Original languageEnglish (US)
Pages (from-to)4586-4601
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number8
StatePublished - Aug 1 2023
Externally publishedYes


  • Consumption Markov decision process (CMDP)
  • planning
  • resource constraints
  • strategy synthesis

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


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