Abstract
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 language | English (US) |
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Pages (from-to) | 712-744 |
Number of pages | 33 |
Journal | SIAM Journal on Control and Optimization |
Volume | 53 |
Issue number | 2 |
DOIs | |
State | Published - 2015 |
Bibliographical note
Publisher Copyright:© 2015 Society for Industrial and Applied Mathematics.
Keywords
- Contiguous visibility
- Discontinuous viscosity solution
- Hamilton-Jacobi
- Hybrid systems
- Integral constraints
- Optimal control
- Reset-renewable resources