Optimal Trajectory Design of Formation Flying based on Attractive Sets

<p>This paper presents a new method of optimal trajectory design for formation flying. Under linearized assumptions and a quadratic performance index, we introduce an attractive set of optimal control based on the linear quadratic regulator theory. The attractive set is defined as a set of all initial states to reach a desired state for a given cost. In particular, we consider attractive sets for two problems: a fixed final-state, fixed final-time problem and an infinite-time problem, and the optimal initial state is found based on the geometry of the attractive set. The optimal trajectories for two problems are evaluated in terms of <i>L</i>₁-norm of control input and termination time.</p>