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.

Automated summary

The purpose of this paper is to propose a Neighboring Optimal Guidance algorithm for driving a dynamical system along an optimal trajectory to a target, even when the Hamiltonian fails to satisfy the strict Legendre condition. This approach addresses problems associated with saturated and bang-bang controls, such as low thrust orbit transfer problems. The author introduces a new formulation of the second-order sufficient conditions for optimality, which allows for tractable solutions to problems with irregular Hamiltonians. The effectiveness of the proposed guidance scheme is successfully demonstrated through a space mission scenario involving Neighboring Optimal Guidance in a low-thrust orbit transfer around Earth.