Nonnegativity criterion for a degenerate quadratic form with two-dimensional control (Q1776281)

The author considers the simplest nontrivial example of a second-order fixed end linear-quadratic problem with the degenerate Legendre condition in the finite optimization horizon. By using a sequence of transformations of state and control variables and changing a time-scale the functional is rewritten in the form which has ``good'' (in the sense of problem regularity) coefficients but the optimization horizon is infinite. Although such problem still may have singularities the author has found exact formulas for the nonnegativity of the functional for the second-order systems. Moreover, relations with the theory of conjugate points and so-called ``frequency criterion'' are shown.