diff --git a/README.md b/README.md index 6aa86f03b395c64bcecb5a23a203daf91dfafaa7..17e6702379bce8a5ba5b39c4a2068570b51ce859 100644 --- a/README.md +++ b/README.md @@ -1,18 +1,27 @@ -# Project Description +# Overview This project contains supplemental Matlab code for the article: >M. Thelander Andrén, B. Bernhardsson, A. Cervin and K. Soltesz, ->"On Event-Based Sampling for H2-Optimal Control", In Proc. 56th IEEE Conf. ->on Decision and Control, Melbourne, Australia, 2017 +>"On Event-Based Sampling for LQG-Optimal Control", In Proc. 56th IEEE Conf. +>on Decision and Control, 2017 It demonstrates a numerical method for computing the optimal event-based sampling -scheme for the continious-time LQG problem. The problem is related to an elliptic -convection-diffusion type of partial-differential equation (PDE) with free -boundary, a so called Stefan problem. The PDE is: +scheme for the continious-time LQG problem. The problem is related to an +elliptic, convection-diffusion type of partial-differential equation +(PDE) with free boundary, a so called Stefan problem. The PDE is: -'''math -x_H^\intercalQx_H -''' +```math + \forall x_{\text{\tiny H}}\in \mathbb{R}^n: \begin{cases} + x_{\text{\tiny H}}^\intercal Qx_{\text{\tiny H}} - J + x_{\text{\tiny H}}^\intercal A^\intercal \nabla V + \frac{1}{2}\text{Tr}(R\nabla^2V) = 0, \\ + V(x_{\text{\tiny H}})\leq \rho + V(0), + \end{cases}\quad\quad + \forall x_{\text{\tiny H}} \in \partial \Omega: + \begin{cases} + V(x_{\text{\tiny H}}) = \rho + V(0),\\ + \nabla V = 0. + \end{cases} +``` -The solution to this PDE is the value function $V$, and the free boundary -$\partial\Omega$ \ No newline at end of file +The solution to this PDE is the value function $`V`$, and the free boundary +$`\partial \Omega`$ is the threshold on the state $`x_{\text{\tiny H}}`$ which +defines the optimal sampling scheme. For more details, we refer to the [article](cdc2017_paper.pdf). \ No newline at end of file