Robust Linear Quadratic Regulator for uncertain systems

This paper develops a Linear Quadratic Regulator (LQR), which is robust to disturbance variability, by using the total variation distance as a metric. The robust LQR problem is formulated as a minimax optimization problem, resulting in a robust optimal controller which in addition to minimizing the quadratic cost it also minimizes the level of disturbance variability. A procedure for solving the LQR problem is also proposed and an example is presented which clearly illustrates the effectiveness of our developed methodology.