# Finite-Horizon Covariance Control of Linear Time-Varying Systems

arXiv: https://arxiv.org/abs/1707.04729 · HTML: https://mlsanity.com/paper/1707.04729/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2017.

## Built on by (most cited first, 5 of 5)

- [Maximum entropy optimal density control of discrete-time linear systems and Schr"odinger bridges](https://mlsanity.com/paper/2204.05263/) (2022)
- [Advancing Trajectory Optimization with Approximate Inference: Exploration, Covariance Control and Adaptive Risk](https://mlsanity.com/paper/2103.06319/) (2021)
- [Efficient Stochastic Optimal Control through Approximate Bayesian Input Inference](https://mlsanity.com/paper/2105.07693/) (2021)
- [On the Convexity of Discrete Time Covariance Steering in Stochastic Linear Systems with Wasserstein Terminal Cost](https://mlsanity.com/paper/2103.13579/) (2021)
- [Mode Reduction for Markov Jump Systems](https://mlsanity.com/paper/2205.02697/) (2022)

## Abstract (arXiv)

We consider the problem of finite-horizon optimal control of a discrete linear time-varying system subject to a stochastic disturbance and fully observable state. The initial state of the system is drawn from a known Gaussian distribution, and the final state distribution is required to reach a given target Gaussian distribution, while minimizing the expected value of the control effort. We derive the linear optimal control policy by first presenting an efficient solution for the diffusion-less case, and we then solve the case with diffusion by reformulating the system as a superposition of diffusion-less systems. This reformulation leads to a simple condition for the solution, which can be effectively solved using numerical methods. We show that the resulting solution coincides with a LQG problem with particular terminal cost weight matrix. This fact provides an additional justification for using a linear in state controller. In addition, it allows an efficient iterative implementation of the controller.