1 research outputs found
Mean and variance of the LQG cost function
Linear Quadratic Gaussian (LQG) systems are well-understood and methods to
minimize the expected cost are readily available. Less is known about the
statistical properties of the resulting cost function. The contribution of this
paper is a set of analytic expressions for the mean and variance of the LQG
cost function. These expressions are derived using two different methods, one
using solutions to Lyapunov equations and the other using only matrix
exponentials. Both the discounted and the non-discounted cost function are
considered, as well as the finite-time and the infinite-time cost function. The
derived expressions are successfully applied to an example system to reduce the
probability of the cost exceeding a given threshold