Update README.md

README.md

-# 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
-$\partial\Omega$
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+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).
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