On the minimum fuel control problem for discrete systems

It is known that the minimum fuel control problem is equivalent to a minimum l1 norm problem with linear equality constraints. By applying the dual space theory of linear vector spaces, the minimum l1 norm can be found by maximizing a linear functional with a l?? norm constraint. This maximization enables the application of a linear programming technique which is usually very efficient. The control sequence which achieves the minimum fuel cost is then found by applying the alignment property in the dual space.