# Mean and variance of the LQG cost function

arXiv: https://arxiv.org/abs/1602.02524 · HTML: https://mlsanity.com/paper/1602.02524/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2016.

## Built on by (most cited first, 1 of 1)

- [Managing Temporal Resolution in Continuous Value Estimation: A Fundamental Trade-off](https://mlsanity.com/paper/2212.08949/) (2022)

## Abstract (arXiv)

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.