Optimal control with budget constraints and resets

R. Takei, W. Chen, Z. Clawson, S. Kirov, A. Vladimirsky

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We consider both discrete and continuous control problems constrained by a fixed budget of some resource, which may be renewed upon entering a preferred subset of the state space. In the discrete case, we consider deterministic shortest path problems on graphs with a full budget reset in all preferred nodes. In the continuous case, we derive augmented PDEs of optimal control, which are then solved numerically on the extended state space with a full/instantaneous budget reset on the preferred subset. We introduce an iterative algorithm for solving these problems efficiently. The method's performance is demonstrated on a range of computational examples, including optimal path planning with constraints on prolonged visibility by a static enemy observer.

Original languageEnglish (US)
Pages (from-to)712-744
Number of pages33
JournalSIAM Journal on Control and Optimization
Issue number2
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.


  • Contiguous visibility
  • Discontinuous viscosity solution
  • Hamilton-Jacobi
  • Hybrid systems
  • Integral constraints
  • Optimal control
  • Reset-renewable resources


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