Contributions to the theory of optimal control

This paper was in fact the first to introduce the RDE as an algorithm for computing the state feedback gain of the optimal controller for a general linear system with a quadratic performance criterion. RDE had emerged earlier in the study of the second variations in the calculus of variations, but its use in general linear systems, where the optimal trajectory needs to be generated by a control input, was new. The analysis throughout the paper concentrates on timevarying systems, and uses the Hamilton-Jacobi theory to arrive at RDE and to deduce optimality of the LQ control gain. We now know, however, that an alternative way to prove optimality in least squares is by showing how RDE allows one to "complete the square" (see, e.g., [5], [18]).