On–off minimum-time control with limited fuel usage: near global optima via linear programming

A method for finding a global optimum to the on–off minimum-time control problem with limited fuel usage is presented. Each control can take on only three possible values: maximum, zero, or minimum. The simplex method for linear systems naturally yields nearly such a solution for the re-formulation presented herein because the simplex method always produces an extreme point solution to the linear program. Numerical examples for the benchmark linear flexible system are presented.