  The goal of this paper is to study a multi-objective linear quadratic
Gaussian (LQG) control problem. In particular, we consider an optimal control
problem minimizing a quadratic cost over a finite time horizon for linear
stochastic systems subject to control energy constraints. To solve the problem,
we suggest an efficient bisection line search algorithm which is
computationally efficient compared to other approaches such as the semidefinite
programming. The main idea is to use the Lagrangian function and
Karush-Kuhn-Tucker (KKT) optimality conditions to solve the constrained
optimization problem. The Lagrange multiplier is searched using the bisection
line search. Numerical examples are given to demonstrate the effectiveness of
the proposed methods.
