2023/11/09 by Maksim Buzikov, Buzikov, Maksim E., Alina M. Mayer +1
Engineering · #49J15 #49M15 #65H05 #FOS: Mathematics #Guidance and Control Systems #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2311.05264
openalex publication_date 2023/11/09 · openalex created_date 2023/11/11 · openalex updated_date 2026/07/28
In this paper we investigated a model that describes the motion of a material point in a viscous medium under a force that is arbitrary in direction, but limited in magnitude. This model was named "the isotropic rocket" in the early work of Rufus Isaacs. We obtained a parametric description of a reachable set for the isotropic rocket and solved a group of reachability problems for a final configuration that varies in a known time-dependent manner (moving target). To describe the reachable set, we obtained an explicit parametric form of its boundary and all its projections onto all subspaces of the state space. Convergent algorithms have been proposed for computing minimum-time interception in position and velocity spaces. Finally, we numerically investigated particular cases of minimum-time interception, validating the development of this study.