On the Jacobi condition for optimizing an engineering problem

摘要

In this paper important properties of the conjugate points are discussed and illustrated for the problem of optimizing the control of a direct-current electric motor. These properties are shown to have significant implications for the optimization problems.The conjugate point nearest to the initial time determine the maximum duration of an optimal control for this process.In a previous study of this problem the conjugate points were not considered and the obtained trajectories were assumed to be optimal.