3 Control of Mechanical Systems from Aerospace Engineering

Abstract

The objective of this chapter is to describe geometric methods applied to aerospace systems: attitude control of a rigid spacecraft, orbital transfer, shuttle re-entry. We characterize the controllability of a rigid spacecraft controlled by one gas jet and the set of orbits reached in orbital transfer, depending upon the orientation of the thrust. Then we construct controls in orbital transfer and attitude control, using stabilization techniques and path planning. The optimal control is analyzed in orbital transfer, the cost being the time and in the shuttle re-entry, where the cost is the total amount of thermal flux, taking into account the state constraints. We present an analysis of extremals, solutions of the maximum principle and second-order sufficient optimality conditions.