From ca7b888d9ac236b68b6364ecfa047f97ac3faa4e Mon Sep 17 00:00:00 2001
From: Atsushi Sakai <asakai.amsl+github@gmail.com>
Date: Mon, 16 Jul 2018 21:31:40 +0900
Subject: [PATCH] update notebook

---
 .../notebook.ipynb                                 | 14 ++++++++++++--
 1 file changed, 12 insertions(+), 2 deletions(-)

diff --git a/PathTracking/model_predictive_speed_and_steer_control/notebook.ipynb b/PathTracking/model_predictive_speed_and_steer_control/notebook.ipynb
index 541206a9..ee700ce1 100644
--- a/PathTracking/model_predictive_speed_and_steer_control/notebook.ipynb
+++ b/PathTracking/model_predictive_speed_and_steer_control/notebook.ipynb
@@ -42,7 +42,9 @@
    "source": [
     "ODE is\n",
     "\n",
-    "$$ \\dot{z} = A'z+B'u$$\n",
+    "$$ \\dot{z} =\\frac{\\partial }{\\partial z} z = A'z+B'u$$\n",
+    "\n",
+    "where\n",
     "\n",
     "\\begin{equation*}\n",
     "A' = \n",
@@ -54,7 +56,15 @@
     "\\end{bmatrix}\n",
     "\\end{equation*}\n",
     "\n",
-    "\n",
+    "\\begin{equation*}\n",
+    "B' =\n",
+    "\\begin{bmatrix}\n",
+    "0 & 0 \\\\\n",
+    "0 & 0 \\\\\n",
+    "1 & 0 \\\\\n",
+    "0 & \\frac{\\bar{v}}{Lcos^2(\\bar{\\delta})} \\\\\n",
+    "\\end{bmatrix}\n",
+    "\\end{equation*}\n",
     "\n",
     "You can get a discrete-time mode with Forward Euler Discretization with sampling time dt.\n",
     "\n",