On the First- and Second-Order Conditions in Optimal Control Problems Related to Autonomous Objects Group lifecycle

摘要

We consider a class of optimal control problems related to target orbiting of autonomous objects group with carrier object use. To describe system dynamics, we use sustem of ODEs consists of two subsystems: “cariier” subsystem and a number of “payload” subsystems. These subsystems are determined on “main” and “nested” time intervals ordered w.r.t. start times. Start time of each “nested” interval is in fact time of corresponding payload decoupling. Our goal is to formulate first- and second-order necessary conditions of extended weak minimum (since we consider variations of decoupling times). To do this, we perfom replication of variables and reduce our OCP to classical form, then rewriting stationarity conditions and quadratic form in original time.