akbar dehghan nezhad - Iran University of Science and Technology
mohammadali rastegar - Iran University of Science and Technology,

Due to the high non-linearity of aerospace control system and the existence of chattering phenomenon, the standard techniques of optimal control do not provide adequatesolutions to this problem. This article will explain how the geometric control techniques are used to analyze the extremals of the problem and to show the existence ofchattering phenomenon. Some classical techniques of optimal control have been recalled, including Pontryagin Maximum Principle, first and second-order optimalityconditions. Techniques of geometric optimal control have then been recalled. such as higher-order optimality conditions and singular controls. We would like to formulate optimal control problem on other manifolds like banach manifold. Practically this is a stronger tool for analyzing the optimal problem. Also apply the modern geometric optimal control for controlling airborne launch vehicle which is completely new and essential.

high optimality condition, chartering phenomenon, geometric optimal control