On the existence of an optimal synthesis for linear quadratic optimal control problems with a fixed terminal point

Abstract

In this paper, we use the dynamic programming and approximation techniques to prove the existence of an optimal synthesis for linear quadratic optimal control (LQOC) problems with a fixed terminal point, in which the optimal control law is given in the feedback form of time and state. Our result establishes an analogy in synthesizing LQOC between fixed terminal point problems and free terminal point problems.