{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Hypersensitive OCP**\n",
    "(c) 2023 Devakumar Thammisetty\n",
    "\n",
    "MPOPT is an open-source Multi-phase Optimal Control Problem (OCP) solver based on pseudo-spectral collocation with customized adaptive grid refinement techniques.\n",
    "\n",
    "https://mpopt.readthedocs.io/\n",
    "\n",
    "Download this notebook: [hypersensitive.ipynb](https://github.com/mpopt/mpopt/blob/docs/docs/source/notebooks/hypersensitive.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Install mpopt from pypi using the following. Disable after first usage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import mpopt (Contains main solver modules)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install mpopt\n",
    "from mpopt import mp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining OCP\n",
    "\n",
    "Hypersensitive OCP:\n",
    "https://www.gpops2.com/Examples/HyperSensitive.html\n",
    "\n",
    "   \\begin{aligned}\n",
    "&\\min_{x, u}        & \\qquad & J = 0 + \\dfrac{1}{2}\\int_{t_0}^{t_f} (x^2 + u^2) \\ dt\\\\\n",
    "&\\text{subject to} &      & \\dot{x} = -x^3 + u\\\\\n",
    "&                  &      & x_0(t_0) = 1; t_0 = 0;\\\\\n",
    "&                  &      & x_1(t_f) = 0; t_f = 1000\n",
    "  \\end{aligned}\n",
    "\n",
    "\n",
    "We first create an OCP object and then polulate the object with dynamics, path_constraints, terminal_constraints and objective (running_costs, terminal_costs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ocp = mp.OCP(n_states=1, n_controls=1, n_phases=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ocp.dynamics[0] = lambda x, u, t: [-x[0] * x[0] * x[0] + u[0]]\n",
    "ocp.running_costs[0] = lambda x, u, t: 0.5 * (x[0] * x[0] + u[0] * u[0])\n",
    "ocp.terminal_constraints[0] = lambda xf, tf, x0, t0: [xf[0] - 1.0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initial state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ocp.x00[0] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Box constraints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "ocp.lbtf[0] = ocp.ubtf[0] = 1000.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scale the time variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "ocp.scale_t = 1 / 1000.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ocp.validate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve and plot the results in one line\n",
    "\n",
    "Lets solve the OCP using following pseudo-spectral approximation\n",
    "* Collocation using Legendre-Gauss-Radau roots\n",
    "* Let's plot the position and velocity evolution with time starting from 0.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "******************************************************************************\n",
      "This program contains Ipopt, a library for large-scale nonlinear optimization.\n",
      " Ipopt is released as open source code under the Eclipse Public License (EPL).\n",
      "         For more information visit http://projects.coin-or.org/Ipopt\n",
      "******************************************************************************\n",
      "\n",
      "Total number of variables............................:      501\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:        0\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:      252\n",
      "Total number of inequality constraints...............:        0\n",
      "        inequality constraints with only lower bounds:        0\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:        0\n",
      "\n",
      "\n",
      "Number of Iterations....: 12\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:   1.1498050755273090e+00    1.1498050755273090e+00\n",
      "Dual infeasibility......:   4.7184478546569153e-16    4.7184478546569153e-16\n",
      "Constraint violation....:   1.4589005542615039e-14    1.1368683772161603e-13\n",
      "Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00\n",
      "Overall NLP error.......:   1.4589005542615039e-14    1.1368683772161603e-13\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 30\n",
      "Number of objective gradient evaluations             = 13\n",
      "Number of equality constraint evaluations            = 42\n",
      "Number of inequality constraint evaluations          = 0\n",
      "Number of equality constraint Jacobian evaluations   = 13\n",
      "Number of inequality constraint Jacobian evaluations = 0\n",
      "Number of Lagrangian Hessian evaluations             = 12\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      0.066\n",
      "Total CPU secs in NLP function evaluations           =      0.010\n",
      "\n",
      "EXIT: Optimal Solution Found.\n",
      "      solver  :   t_proc      (avg)   t_wall      (avg)    n_eval\n",
      "       nlp_f  | 340.00us ( 11.33us) 340.41us ( 11.35us)        30\n",
      "       nlp_g  |   4.85ms (115.38us)   4.78ms (113.76us)        42\n",
      "    nlp_grad  | 266.00us (266.00us) 265.36us (265.36us)         1\n",
      "  nlp_grad_f  | 322.00us ( 23.00us) 322.67us ( 23.05us)        14\n",
      "  nlp_hess_l  | 592.00us ( 49.33us) 595.87us ( 49.66us)        12\n",
      "   nlp_jac_g  |   2.76ms (197.43us)   2.75ms (196.68us)        14\n",
      "       total  |  76.82ms ( 76.82ms)  76.14ms ( 76.14ms)         1\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mpo, post = mp.solve(ocp, n_segments=5, poly_orders=50, scheme=\"LGR\", plot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Retrive the solution*\n",
    "\n",
    "x: states, u: Controls, t:time, a:Algebraic variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal time, state : 1000.0000 vs 1000 (Exact), [1.]\n"
     ]
    }
   ],
   "source": [
    "x, u, t, a = post.get_data()\n",
    "print(f\"Terminal time, state : {t[-1][0]:.4f} vs 1000 (Exact), {x[-1]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve again with Chebyshev-Gauss-Lobatto (CGL) roots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of variables............................:      501\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:        0\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:      252\n",
      "Total number of inequality constraints...............:        0\n",
      "        inequality constraints with only lower bounds:        0\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:        0\n",
      "\n",
      "\n",
      "Number of Iterations....: 12\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:   1.1406025536022588e+00    1.1406025536022588e+00\n",
      "Dual infeasibility......:   5.5128124287762148e-13    5.5128124287762148e-13\n",
      "Constraint violation....:   5.6878507039202523e-12    1.8587797967484221e-11\n",
      "Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00\n",
      "Overall NLP error.......:   5.6878507039202523e-12    1.8587797967484221e-11\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 36\n",
      "Number of objective gradient evaluations             = 13\n",
      "Number of equality constraint evaluations            = 49\n",
      "Number of inequality constraint evaluations          = 0\n",
      "Number of equality constraint Jacobian evaluations   = 13\n",
      "Number of inequality constraint Jacobian evaluations = 0\n",
      "Number of Lagrangian Hessian evaluations             = 12\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      0.061\n",
      "Total CPU secs in NLP function evaluations           =      0.010\n",
      "\n",
      "EXIT: Optimal Solution Found.\n",
      "      solver  :   t_proc      (avg)   t_wall      (avg)    n_eval\n",
      "       nlp_f  | 425.00us ( 11.81us) 407.26us ( 11.31us)        36\n",
      "       nlp_g  |   5.59ms (114.14us)   5.58ms (113.88us)        49\n",
      "    nlp_grad  | 264.00us (264.00us) 263.05us (263.05us)         1\n",
      "  nlp_grad_f  | 325.00us ( 23.21us) 325.10us ( 23.22us)        14\n",
      "  nlp_hess_l  | 614.00us ( 51.17us) 617.11us ( 51.43us)        12\n",
      "   nlp_jac_g  |   2.82ms (201.79us)   2.81ms (201.06us)        14\n",
      "       total  |  78.41ms ( 78.41ms)  77.65ms ( 77.65ms)         1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mpo, post = mp.solve(ocp, n_segments=5, poly_orders=50, scheme=\"CGL\", plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal time, state : 1000.0000 vs 1000s (Exact), [1.]\n"
     ]
    }
   ],
   "source": [
    "x, u, t, a = post.get_data()\n",
    "print(f\"Terminal time, state : {t[-1][0]:.4f} vs 1000s (Exact), {x[-1]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve again with Legendre-Gauss-Lobatto (LGL) roots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of variables............................:      501\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:        0\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:      252\n",
      "Total number of inequality constraints...............:        0\n",
      "        inequality constraints with only lower bounds:        0\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:        0\n",
      "\n",
      "\n",
      "Number of Iterations....: 12\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:   1.1502075893651909e+00    1.1502075893651909e+00\n",
      "Dual infeasibility......:   1.0234087882698972e-13    1.0234087882698972e-13\n",
      "Constraint violation....:   4.7414571594509346e-13    1.3997691894473974e-12\n",
      "Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00\n",
      "Overall NLP error.......:   4.7414571594509346e-13    1.3997691894473974e-12\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 36\n",
      "Number of objective gradient evaluations             = 13\n",
      "Number of equality constraint evaluations            = 49\n",
      "Number of inequality constraint evaluations          = 0\n",
      "Number of equality constraint Jacobian evaluations   = 13\n",
      "Number of inequality constraint Jacobian evaluations = 0\n",
      "Number of Lagrangian Hessian evaluations             = 12\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      0.064\n",
      "Total CPU secs in NLP function evaluations           =      0.011\n",
      "\n",
      "EXIT: Optimal Solution Found.\n",
      "      solver  :   t_proc      (avg)   t_wall      (avg)    n_eval\n",
      "       nlp_f  | 423.00us ( 11.75us) 431.21us ( 11.98us)        36\n",
      "       nlp_g  |   6.12ms (124.82us)   6.12ms (124.86us)        49\n",
      "    nlp_grad  | 264.00us (264.00us) 263.12us (263.12us)         1\n",
      "  nlp_grad_f  | 326.00us ( 23.29us) 327.97us ( 23.43us)        14\n",
      "  nlp_hess_l  | 611.00us ( 50.92us) 610.94us ( 50.91us)        12\n",
      "   nlp_jac_g  |   2.82ms (201.07us)   2.82ms (201.54us)        14\n",
      "       total  |  77.49ms ( 77.49ms)  76.93ms ( 76.93ms)         1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mpo, post = mp.solve(ocp, n_segments=5, poly_orders=50, scheme=\"LGL\", plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal time, state : 1000.0000 vs 1000s (Exact), [1.]\n"
     ]
    }
   ],
   "source": [
    "x, u, t, a = post.get_data()\n",
    "print(f\"Terminal time, state : {t[-1][0]:.4f} vs 1000s (Exact), {x[-1]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}