Periodic optimal flight

For a host of dynamic systems, periodic motion is more efficient than steady-state operation. This work focuses on atmospheric fuel-efficient periodic flight. To understand some of the generic properties of periodic optimal flight, the theoretical aspects are presented, which form the basis for the numerical computation of periodic optimal paths. Furthermore, the simplest problem for which periodic optimal control can be induced is formulated and various solutions based on asymptotic analysis are given. Intuitive physical mechanisms that contribute to producing periodic optimal flight are discussed on the basis of various levels of approximation of the aircraft dynamic models and upon perturbation analysis about the steady-state cruise path. The performance improvement and the dramatic periodic optimal flight path of a hypersonic vehicle are computed. To mechanize this flight path, a neighbouring optimum perturbation guidance law is developed and its performance is presented.