Control of Affine Nonlinear Systems with Nilpotent Structure in Singular Problems

The minimum singular functional control problem is analyzed for a class of multi-input affine nonlinear systems under the hypothesis that the associated Lie algebra is nilpotent. The optimal control corresponding to the first, second, and third order nilpotent operators is determined. We develop an algorithm for solving the singular problem that is applicable whether or not singular subarcs exist in the optimal control.This work was partial supported by the Romanian Aerospace Agency, Grant 31032.