From edb25530179092cad01882a2b2675107d310da1b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Marcus=20Thelander=20Andr=C3=A9n?=
<marcus.thelander_andren@control.lth.se>
Date: Thu, 21 Sep 2017 17:45:33 +0200
Subject: [PATCH] Update README.md
---
README.md | 31 ++++++++++++++++++++-----------
1 file changed, 20 insertions(+), 11 deletions(-)
diff --git a/README.md b/README.md
index 6aa86f0..17e6702 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
--
GitLab