Neighboring Optimal Guidance in Bang Bang Control with Target

The purpose of this paper is to present a Neighboring Optimal Guidance algorithm capable of driving a dynamical system along an optimal trajectory to a target when the Hamiltonian fails to satisfy the strict Legendre condition. Similar problems are associated with saturated and bang–bang controls as, for instance, in the case of low thrust orbit transfer problems. The approach is based on a new formulation of the second-order sufficient conditions for optimality—introduced by the author—which make tractable, problems with irregular Hamiltonians. Effectiveness of the guidance scheme proposed in this work is successfully tested on a space mission scenario, i.e. Neighboring Optimal Guidance in a low-thrust orbit transfer about Earth.