update notebook

Author: AtsushiSakai

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",