On the uniqueness of the extremal controls for a class of minimum fuel problems

The purpose of this paper is to investigate the uniqueness of the extremal controls, i.e., the controls which satisfy the necessary conditions provided by the maximum principle, for a class of minimum fuel problems pertaining to the control of single input, linear, time-invariant systems. Sufficient conditions for a fuel-optimal problem to be normal are given; then it is shown that the normal extremal controls can be unique under suitable assumptions.