  Although the classical LQR design method has been very successful in real
world engineering designs, in some cases, the classical design method needs
modifications because of the saturation in actuators. This modified problem is
sometimes called the constrained LQR design. For discrete systems, the
constrained LQR design problem is equivalent to a convex quadratic programming
problem with box constraints. We will show that the interior-point method is
very efficient for this problem because an initial interior point is available,
a condition which is not true for general convex quadratic programming problem.
We will devise an effective and efficient algorithm for the constrained LQR
design problem using the special structure of the box constraints and a
recently introduced arc-search technique for the interior-point algorithm. We
will prove that the algorithm is polynomial and has the best-known complexity
bound for the convex quadratic programming. The proposed algorithm is
implemented in MATLAB. An example for the constrained LQR design is provided to
show the effectiveness and efficiency of the design method. The proposed
algorithm can easily be used for model predictive control.
