Fields of extremals in linear-quadratic problems of optimal control

Abstract

The author presents necessary and sufficient conditions for optimality of extremals in linear-quadratic problems of optimal control. He shows by an example that when the second variation is only semipositive definite and extremals are still minimizers, the classical Riccati equation technique fails. The conditions obtained allow one to solve linear-quadratic problems with subsidiary conditions. An example of a solution to a constrained problem is presented.<>