Abstract
The minimization control problem of quadratic functionals for the
class of affine nonlinear systems with the hypothesis of nilpotent
associated Lie algebra is analyzed. The optimal control
corresponding to the first-, second-, and third-order nilpotent
operators is determined. In this paper, we have considered the
minimum fuel problem for the multi-input nilpotent control and for
a scalar input bilinear system for such systems. For the
multi-input system, usually an analytic closed-form solution for
the optimal control