Title: Linear Quadratic Optimal Control Problems with Fixed Terminal States and Integral Quadratic Constraints,
Abstract: This paper is concerned with a linear quadratic (LQ, for short) optimal
control problem with fixed terminal states and integral quadratic constraints.
A Riccati equation with infinite terminal value is introduced, which is
uniquely solvable and whose solution can be approximated by the solution for a
suitable unconstrained LQ problem with penalized terminal state. Using results
from duality theory, the optimal control is explicitly derived by solving the
Riccati equation together with an optimal parameter selection problem. It turns
out that the optimal control is not only a feedback of the current state, but
also a feedback of the target (terminal state). Some examples are presented to
illustrate the theory developed.