2011/10/28 by Ryo Takei, Weiyan Chen, Takei, Ryo +7 · 1 citation
Computer Science · Engineering · Mathematics · #34A38 #49L20 #49L25 #49N90 #65K05 #65N22 #90C29 #Advanced Control Systems Optimization #FOS: Computer and information sciences #FOS: Mathematics #G.1.8 #I.2.8 #Optimization and Control (math.OC) #Optimization and Variational Analysis #Robotics (cs.RO) #acm:34A38 #acm:49L20 #acm:49L25 #acm:49N90 #acm:65K05 #acm:65N22 #acm:90C29 #cs.RO #math.OC #msc:34A38 #msc:49L20 #msc:49L25 #msc:49N90 #msc:65K05 #msc:65N22 #msc:90C29
paper · pdf · doi:10.48550/arxiv.1110.6221
31 pages, 13 figures; accepted by SIAM J. on Control & Optimization (updated to address reviewers' comments)
openalex publication_date 2011/10/28 · arxiv created 2014/09/27 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 both deterministic and stochastic shortest path problems with full budget resets 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 the optimal path planning with constraints on prolonged visibility by a static enemy observer. In addition, we also develop an algorithm that works on the original state space to solve a related but simpler problem: finding the subsets of the domain "reachable-within-the-budget". This manuscript is an extended version of the paper accepted for publication by SIAM J. on Control and Optimization. In the journal version, Section 3 and the Appendix were omitted due to space limitations.