High-speed yo-yo maneuvers as bang-bang solutions

Abstract

The purpose of this paper is to study an aircraft pursuit problem as an optimal control problem and analyze the resulting optimal pursuit trajectories, i.e., the yo-yo maneuver, to study the controls of the maneuver. Generally speaking, the optimization of aircraft maneuvers is formulated as the minimum-time problem, and the optimal trajectories often result in typical bang-bang control solutions within several constraints, which are not easily converged in numerical analysis. Best way to avoid the numerical difficulties of the discontinuous controls is dividing the trajectory into subarcs, in which the controls are piece-wise constant, but that leads to another difficulty, known as the multi-point boundary value problem in the optimal control problem. In this paper, a formulation called Folded Time Axis Method is applied to convert the multi-point boundary value problem to a two point boundary value problem. We have many general numerical methods to solve the two point boundary value problem in the optimal control problem. The solutions result in the high speed yo-yo maneuver, because the target airplane flies at less speed than the chaser does at this time. Nomenciature