From 5b019d0aa7a907e23917955ca6e34ae6533d7ebd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Marcus=20Thelander=20Andr=C3=A9n?=
 <marcus.thelander_andren@control.lth.se>
Date: Fri, 9 Nov 2018 17:05:56 +0100
Subject: [PATCH] Initial update of README.md

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 README.md | 19 ++++++++++++++++++-
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-# rbf-approx
+# Overview
+This project contains supplemental Matlab code for the article:
 
+>M. Thelander Andrén, "Using Radial Basis Functions to Appriximate the LQG-Optimal Event-Based Sampling Policy", 
+Submitted to European Control Conference, 2019
+
+It demonstrates a numerical method using radial basis functions (RBF) to compute
+an approximation of the optimal event-based sampling policy for the continuous-time
+sampled-data LQG problem. The optimal policy is given by the solution to a stationary
+partial differential equation (PDE) with free boundary. The PDE is given by:
+
+```math
+-V(\tilde{x}^\intercal Q\tilde{x} - J + \tilde{x}^\intercal A^\intercal\nabla V + \frac{1}{2}\Delta V) = 0,\quad \forall \tilde{x}, 
+```
+```math
+-V\geq 0, \quad \tilde{x}^\intercal Q\tilde{x} - J + \tilde{x}^\intercal A^\intercal\nabla V + \frac{1}{2}\Delta V\geq 0, \quad \forall \tilde{x}.
+```
+The solution to this PDE is the relative value function $`V:\tilde{x}\rightarrow\mathbb{R}`$, and the optimal sampling policy is to trigger sampling whenever $`V(\tilde{x})=0`$ holds.
+For more details we refer to our [article](ecc2019_paper.pdf).
-- 
GitLab