The balance and harmony of control power for combat aircraft attitude-maneuvers

In some cases, time-optimal aircraft roll-maneuvers exhibit a nonintuitive feature, in which the extremal roll-control causes the vehicle to initially roll the wrong way. An explanation of this and related phenomena is presented. The analysis is based on the concepts of control balance and state coupling within a dynamical system, and harmony between the control balance and the extremal maneuver. These ideas are quite general and applicable to many optimal control problems. The concept of evolution of an extremal solution is adopted as the basic tool in the analysis. Various levels of dynamical coupling are identified within the combat-aircraft attitude model, and the characteristic extremal-family motion is explained