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   "source": [
    "# Model predictive speed and steering control"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MPC modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vehicle model linearization\n",
    "\n",
    "State vector is:\n",
    "$$ x = [x, y, v,\\phi]$$ x: x-position, y:y-position, v:velocity, φ: yaw angle\n",
    "\n",
    "Input vector is:\n",
    "$$ u = [a, \\delta]$$ a: accellation, δ: steering angle\n",
    "\n",
    "Vehicle model is \n",
    "$$ \\dot{x} = vcos(\\phi)$$\n",
    "$$ \\dot{y} = vsin((\\phi)$$\n",
    "$$ \\dot{v} = a$$\n",
    "$$ \\dot{\\phi} = \\frac{vtan(\\delta)}{L}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reference\n",
    "\n",
    "- [Vehicle Dynamics and Control \\| Rajesh Rajamani \\| Springer](http://www.springer.com/us/book/9781461414322)\n",
    "\n",
    "- [MPC Course Material \\- MPC Lab @ UC\\-Berkeley](http://www.mpc.berkeley.edu/mpc-course-material)\n"
   ]
  }
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