Optimal trajectory, guidance, and conjugate points

Two interesting and important properties of the conjugate points have been discussed and illustrated by means of examples. These properties are shown to have significant implications for trajectory and guidance optimization problems.The conjugate point nearest to the initial time determines the maximum duration of an optimal control for a linear process with a quadratic cost functional and for a certain nonlinear process.If there is a conjugate point to the terminal time, then it is not possible to construct the linear, optimal guidance system in a neighborhood of the nominal trajectory