ON THE OPTIMAL CONTROL OF QUADRATIC FUNCTIONALS FOR AFFINE NILPOTENT SYSTEMS

Abstract

The minimization control problem of quadratic functionals for he 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 operator is determined. In this paper we have considered the minimum fuel problem for the multiinput control and for a scalar input bilinear system for such systems. For the multiinput system, usually an analytic closed-form solution for the optimal control is not possible and it is necessary to use numerical integration for the set of m nonlinear coupled second order differential eqations. The optimal control of bilinear systems is obtained by considering the Lie algebra generated by the system matrices. It should be noted that we have obtained an open-lop control depending on the initial value of the state .