ME_C231A_Final_Project.ipynb

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  "metadata": {
    "colab": {
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      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/waynechu1109/ME-C231A-Final-Project/blob/main/ME_C231A_Final_Project.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Dependencies Installation\n",
        "**Run the code below every time before working on the project.**:"
      ],
      "metadata": {
        "id": "CspKt-I6loRv"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-Z2am6Sgk8_o",
        "outputId": "27a75bc6-70c5-46a4-a7c9-0d4dc6c35231"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "  Created wheel for polytope: filename=polytope-0.2.4-py3-none-any.whl size=47673 sha256=47bec9037c0ec792f036449d59b3abbd4654ec76fa4a7ffa1f9910a64b56a7d3\n",
            "  Stored in directory: /root/.cache/pip/wheels/9b/de/92/9d58cc85957b1657fe6b2e134016350f9311361eaddc4e6d29\n",
            "Successfully built polytope\n",
            "Installing collected packages: numpy, polytope\n",
            "  Attempting uninstall: numpy\n",
            "    Found existing installation: numpy 1.23.5\n",
            "    Uninstalling numpy-1.23.5:\n",
            "      Successfully uninstalled numpy-1.23.5\n",
            "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
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            "lida 0.0.10 requires python-multipart, which is not installed.\n",
            "lida 0.0.10 requires uvicorn, which is not installed.\u001b[0m\u001b[31m\n",
            "\u001b[0mSuccessfully installed numpy-1.26.2 polytope-0.2.4\n",
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            "/sbin/ldconfig.real: /usr/local/lib/libtbb.so.12 is not a symbolic link\n",
            "\n",
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            "\n"
          ]
        }
      ],
      "source": [
        "# # install required dependencies\n",
        "#import sys\n",
        "!pip install polytope\n",
        "!pip install -q pyomo\n",
        "!apt-get install -y -qq glpk-utils\n",
        "!apt-get install -y -qq coinor-cbc\n",
        "!wget -N -q \"https://github.com/thomasfork/ipopt_linux/raw/main/ipopt-linux64.zip\"\n",
        "!unzip -o -q ipopt-linux64\n",
        "\n",
        "# IN_COLAB = 'google.colab' in sys.modules\n",
        "# if IN_COLAB:\n",
        "  #!pip install polytope"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Linearize the function"
      ],
      "metadata": {
        "id": "Mio_EwGrD-9l"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# (z1, z2, z3, z4) -> (p, x, y, q) -> (x, h, vx, xh)\n",
        "# (u1, u2) -> (u, r)\n",
        "import sympy as sp\n",
        "import numpy as np\n",
        "\n",
        "# Define the variables\n",
        "z1, z2, z3, z4, u1, u2 = sp.symbols('z1 z2 z3 z4 u1 u2')\n",
        "Ts = 1\n",
        "frho = (1-(2.2558*10**-5)*z2)**4.2577\n",
        "fw = 0.00879*(z2-9000)+51.39\n",
        "\n",
        "S = 125\n",
        "Cd = 0.053\n",
        "w = 70000\n",
        "C = S*Cd/w\n",
        "g = 9.77\n",
        "\n",
        "# Define the function (replace with your actual function)\n",
        "g1 = z1+Ts*z3\n",
        "g2 = z2+Ts*z4\n",
        "g3 = z3+Ts*((u1)-(1/2)*frho*(z3**2 + fw**2)*C)\n",
        "g4 = z4 + Ts*(u2-g)\n",
        "\n",
        "# Calculate partial derivatives\n",
        "\n",
        "# g1\n",
        "dg1_dp = sp.diff(g1, z1)\n",
        "# dg1_dx = sp.diff(g1, z2)\n",
        "dg1_dy = sp.diff(g1, z3)\n",
        "\n",
        "# g2\n",
        "# dg2_dp = sp.diff(g2, z1)\n",
        "dg2_dx = sp.diff(g2, z2)\n",
        "# dg2_dy = sp.diff(g2, z3)\n",
        "dg2_dq = sp.diff(g2, z4)\n",
        "\n",
        "# g3\n",
        "dg3_dx = sp.diff(g3, z2)\n",
        "dg3_dy = sp.diff(g3, z3)\n",
        "dg3_du = sp.diff(g3, u1)\n",
        "\n",
        "# g4\n",
        "dg4_dq = sp.diff(g4, z4)\n",
        "dg4_dr = sp.diff(g4, u2)\n",
        "\n",
        "# Specify the operating point\n",
        "operating_point = {z2: 11000, z3: 150, u1:0}\n",
        "\n",
        "# Evaluate partial derivatives at the operating point\n",
        "dg3_dx_op = dg3_dx.subs(operating_point)\n",
        "dg3_dy_op = dg3_dy.subs(operating_point)\n",
        "\n",
        "dg3_du_op = dg3_du.subs(operating_point)\n",
        "\n",
        "# Linearized A\n",
        "A = np.array([[dg1_dp, 0, dg1_dy, 0],\n",
        "              [0, dg2_dx, 0, dg2_dx],\n",
        "              [0, dg3_dx_op, dg3_dy_op, 0],\n",
        "              [0, 0, 0, dg4_dq]])\n",
        "\n",
        "# Linearized B\n",
        "B = np.array([[0, 0],\n",
        "              [0, 0],\n",
        "              [dg3_du, 0],\n",
        "              [0, dg4_dr]])\n",
        "\n",
        "# Linearize the function\n",
        "linearized_function = g3.subs({z2: operating_point[z2], z3: operating_point[z3], u1: operating_point[u1]}) + dg3_dx_op * (z2 - operating_point[z2]) + dg3_dy_op * (z3 - operating_point[z3]) + dg3_du_op * (u1 - operating_point[u1])\n",
        "\n",
        "# Print the linearized function\n",
        "print(\"Linearized Function:\", linearized_function)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PFOjpL07a_wn",
        "outputId": "9b2e0dd2-038c-4c51-f2c8-e7ba4b0d5fa0"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Linearized Function: u1 + 3.1885933779961e-5*z2 + 0.995784855748938*z3 - 0.101445635669052\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# CFTOC Formulation"
      ],
      "metadata": {
        "id": "kblGoGqxv6jB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Formulation of CFTOC Problem with Pyomo\n",
        "\n",
        "First we will write a function which formulates and solves a finite time optimal control problem with quadratic cost, linear dynamics, and linear constraints. Then we call this function as a part of the MPC controller. Consider the problem defined below:\n",
        "\\begin{equation}\n",
        "\\begin{aligned}\n",
        "\\min_{x_1 \\dots x_N,u_0 \\dots u_{N-1}} & \\quad x_N^{\\top}Px_N+\\sum_{k=0}^{N-1}x_k^{\\top}Qx_k+u_k^{\\top}Ru_k \\\\\n",
        "\\text{s.t.} & \\quad x_{k+1} = Ax_k + Bu_k \\quad \\forall k=0\\dots N-1\\\\\n",
        "& \\quad x_{min} \\leq x_k \\leq x_{max}  \\quad \\forall k=0\\dots N-1 \\\\\n",
        "& \\quad u_{min} \\leq u_k \\leq u_{max}  \\quad \\forall k=0\\dots N-1 \\\\\n",
        "& \\quad x_0 = x(0) \\\\\n",
        "& \\quad x_N \\in \\mathcal{X}_f\n",
        "\\end{aligned}\n",
        "\\end{equation}\n",
        "\n",
        "Write a function in the following form which formulates the problem using pyomo and solves the problem using the solver $\\texttt{ipopt}$. Test your code on several 1 and 2-state examples."
      ],
      "metadata": {
        "id": "VQCgQShaoUzJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "- $\\texttt{feas}$ is a scalar logical indicating the feasibility of the CFTOC problem\n",
        "- $\\texttt{xOpt}$ is a $n_x \\times (N+1)$ matrix of the optimal state trajectory, where $n_x$ is the state dimension\n",
        "- $\\texttt{uOpt}$ is a $n_u \\times N$ matrix of the optimal input sequence, where $n_u$ is the input dimension\n",
        "- $\\texttt{JOpt}$ is a scalar of the optimal cost from the specified initial condition\n",
        "- $\\texttt{A, B}$ are the state and input matricies of the linear dynamics\n",
        "- $\\texttt{P}$ is the terminal cost matrix\n",
        "- $\\texttt{Q, R}$ are the stage cost matricies\n",
        "- $\\texttt{N}$ is the MPC horizon\n",
        "- $\\texttt{x0}$ is the initial condition\n",
        "- $\\texttt{xL, xU, uL, uU}$ are the box state and input constraints\n",
        "- $\\texttt{bf, Af}$ are used to represent the terminal set. If the terminal set ${\\cal X}_f$ is a single point, ${\\cal X}_f = \\{ \\bar{x}_N \\}$, the input argument $\\texttt{bf}$ is used to specify this single point $\\bar{x}_N$, and the input argument $\\texttt{Af = []}$ is used to designate this special case of a single-point terminal set. If the terminal set is described by a set of linear inequalities, it can be expressed using the inequality $A_f x_N \\leq b_f$.\n"
      ],
      "metadata": {
        "id": "-z8yOFLvodHk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**If the cell below cannot run properly, \"Restart Runtime\" then run again.**"
      ],
      "metadata": {
        "id": "sPJSCMTPolpb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import polytope as pt\n",
        "import numpy as np\n",
        "# from __future__ import division\n",
        "import pyomo.environ as pyo\n",
        "import matplotlib.pyplot as plt\n",
        "# %matplotlib widget"
      ],
      "metadata": {
        "id": "ZFu4s_u6oPQ4"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def solve_cftoc(A, B, P, Q, R, N, x0, xref, Af=np.nan, bf=np.nan):\n",
        "\n",
        "\n",
        "    # uref = np.array\n",
        "    xmax = 50000\n",
        "    xmin = 0\n",
        "    hmax = 12000\n",
        "    hmin = 9000\n",
        "    vxmax = 268.54\n",
        "    vxmin = 63.28\n",
        "    vhmax = 15.24\n",
        "    vhmin = -10.16\n",
        "    uxmax = 3.07\n",
        "    uxmin = 0\n",
        "    uhmax = 3.07\n",
        "    uhmin = -3\n",
        "\n",
        "    # xU = np.array([xmax, hmax, vxmax, vhmax])\n",
        "    # xL = np.array([xmin, hmin, vxmin, vhmin])\n",
        "    xMax = np.array([xmax, hmax, vxmax, vhmax]) # upper bound\n",
        "    xMin = np.array([xmin, hmin, vxmin, vhmin])\n",
        "    uMax = np.array([uxmax, uhmax])\n",
        "    uMin = np.array([uxmin, uhmin])\n",
        "\n",
        "\n",
        "    S = 125.0\n",
        "    C_d = 0.053\n",
        "    W = 7e5\n",
        "    model = pyo.ConcreteModel()\n",
        "    model.N = N\n",
        "    rho_0 = 1.225\n",
        "\n",
        "    model.nx = 4\n",
        "    model.nu = 2\n",
        "\n",
        "    model.A = A\n",
        "    model.B = B\n",
        "\n",
        "\n",
        "    # length of finite optimization problem:\n",
        "    model.tIDX = pyo.Set( initialize= range(model.N+1), ordered=True )\n",
        "    model.xIDX = pyo.Set( initialize= range(model.nx), ordered=True )\n",
        "    model.uIDX = pyo.Set( initialize= range(model.nu), ordered=True )\n",
        "\n",
        "    # these are 2d arrays:\n",
        "    model.Q = Q\n",
        "    model.P = P\n",
        "    model.R = R\n",
        "\n",
        "    # Create state and input variables trajectory:\n",
        "    # model.x = pyo.Var(model.xIDX, model.tIDX, bounds=(xL,xU))\n",
        "    model.x = pyo.Var(model.xIDX, model.tIDX)\n",
        "    # model.u = pyo.Var(model.uIDX, model.tIDX, bounds=(uL,uU))\n",
        "    model.u = pyo.Var(model.uIDX, model.tIDX)\n",
        "\n",
        "    #Objective:\n",
        "    def objective_rule(model):\n",
        "        costX = 0.0\n",
        "        costU = 0.0\n",
        "        costTerminal = 0.0\n",
        "        for t in model.tIDX:\n",
        "            for i in model.xIDX:\n",
        "                for j in model.xIDX:\n",
        "                    if t < model.N:\n",
        "                        costX += (model.x[i, t]-xref[i]) * model.Q[i, j] * (model.x[j, t]-xref[j])\n",
        "\n",
        "        for t in model.tIDX:\n",
        "            for i in model.uIDX:\n",
        "                for j in model.uIDX:\n",
        "                    if t < model.N:\n",
        "                        costU += model.u[i, t] * model.R[i, j] * model.u[j, t]\n",
        "\n",
        "        for i in model.xIDX:\n",
        "            for j in model.xIDX:\n",
        "                costTerminal += (model.x[i, model.N]-xref[i]) * model.P[i, j] * (model.x[j, model.N]-xref[j])\n",
        "\n",
        "        return costX + costU + costTerminal\n",
        "\n",
        "    model.cost = pyo.Objective(rule = objective_rule, sense = pyo.minimize)\n",
        "\n",
        "    # Constraints:\n",
        "    def equality_const_rule(model, i, t):\n",
        "        return model.x[i, t+1] - (sum(model.A[i, j] * model.x[j, t] for j in model.xIDX)\n",
        "                               +  sum(model.B[i, j] * model.u[j, t] for j in model.uIDX) ) == 0.0 if t < model.N else pyo.Constraint.Skip\n",
        "\n",
        "    model.equality_constraints = pyo.Constraint(model.xIDX, model.tIDX, rule=equality_const_rule)\n",
        "\n",
        "    # Constraints:\n",
        "    model.init_const1 = pyo.Constraint(expr = model.x[0, 0] == x0[0])\n",
        "    model.init_const2 = pyo.Constraint(expr = model.x[1, 0] == x0[1])\n",
        "    model.init_const3 = pyo.Constraint(expr = model.x[2, 0] == x0[2])\n",
        "    model.init_const4 = pyo.Constraint(expr = model.x[3, 0] == x0[3])\n",
        "\n",
        "    # states boundary\n",
        "    model.constraint1 = pyo.Constraint(model.xIDX, model.tIDX, rule=lambda model, i, t: model.x[i, t] <= xMax[i]\n",
        "                                      if t <= N else pyo.Constraint.Skip)\n",
        "\n",
        "    model.constraint2 = pyo.Constraint(model.xIDX, model.tIDX, rule=lambda model, i, t: model.x[i, t] >= xMin[i]\n",
        "                                      if t <= N else pyo.Constraint.Skip)\n",
        "\n",
        "    model.constraint3 = pyo.Constraint(model.uIDX, model.tIDX, rule=lambda model, i, t: model.u[i, t] <= uMax[i]\n",
        "                                      if t <= N-1 else pyo.Constraint.Skip)\n",
        "\n",
        "    model.constraint4 = pyo.Constraint(model.uIDX, model.tIDX, rule=lambda model, i, t: model.u[i, t] >= uMin[i]\n",
        "                                      if t <= N-1 else pyo.Constraint.Skip)\n",
        "\n",
        "\n",
        "    # # terminal constraints\n",
        "    def final_const_rule(model, i):\n",
        "        return sum(Af[i, j] * model.x[j, N] for j in model.xIDX) <= bf[i]\n",
        "\n",
        "    model.final_const = pyo.Constraint(model.xIDX, rule=final_const_rule)\n",
        "\n",
        "    solver = pyo.SolverFactory('ipopt')\n",
        "    results = solver.solve(model)\n",
        "\n",
        "    if str(results.solver.termination_condition) == \"optimal\":\n",
        "        feas = True\n",
        "    else:\n",
        "        feas = False\n",
        "\n",
        "    xOpt = np.asarray([[model.x[i,t]() for i in model.xIDX] for t in model.tIDX]).T\n",
        "    uOpt = np.asarray([model.u[:,t]() for t in model.tIDX]).T\n",
        "\n",
        "    JOpt = model.cost()\n",
        "\n",
        "    return [model, feas, xOpt, uOpt, JOpt]"
      ],
      "metadata": {
        "id": "6AVytRhooQPo"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# MPC"
      ],
      "metadata": {
        "id": "akQ77IiExCqa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Consider the following system\n",
        "\\begin{equation}\\label{eq:model-int1}\n",
        "x(k+1)=\\begin{bmatrix} 1 &  1\\\\ 0 & 1 \\end{bmatrix}x(k)+\n",
        "     \\begin{bmatrix} 0\\\\ 1 \\end{bmatrix}u(k) \\quad \\quad (1)   \n",
        "\\end{equation}\n",
        "\n",
        "The state and input constraints are\n",
        "\\begin{equation}\\begin{aligned}\n",
        "\\mathcal{U}: &-0.5\\leq u(k)\\leq 0.5 \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad (2a)\\\\\n",
        "\\mathcal{X}: &\\begin{bmatrix} -5\\\\ -5 \\end{bmatrix} \\leq x(k) \\leq \\begin{bmatrix} 5\\\\ 5 \\end{bmatrix} \\quad \\quad \\quad \\quad \\quad \\quad \\quad(2b)\n",
        "\\end{aligned}\n",
        "\\label{eq:con1}\\end{equation}"
      ],
      "metadata": {
        "id": "_YXiTr3Swmym"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this problem, we will design an MPC controllers of the form:\n",
        "\n",
        "\\begin{equation*}\n",
        "   \\begin{array}{lll}\n",
        "       J_0^*(x_0)=  &\\displaystyle{\\min_{{U_0}}}& \\displaystyle{ \\color{red}{x_N'Px_N} + \\sum_{k=0}^{{N}-1}\n",
        "  x_k'Qx_k+u_k'Ru_k} \\\\\n",
        "       &\\text{subject to}   \\\\\n",
        "       &&x_{k+1}=Ax_{k}+Bu_{k},\\ k=0,\\ldots,N-1\\\\\n",
        "                       &&x_{k}\\in\\mathcal{X},~u_{k}\\in\\mathcal{U},~k=0,\\ldots,N-1\\\\\n",
        "                       && \\color{red}{{x_{N}\\in {\\mathcal{X}_f} }} \\\\\n",
        "                       && x_{0}=x(t)\n",
        "    \\end{array}\n",
        "\\end{equation*}\n",
        "In this problem, $Q=I_2$, $R=10$, $P=Q$ and $N=3$. Also, we set $\\mathcal{X_f}=\\mathcal{X}$."
      ],
      "metadata": {
        "id": "0LM3EwC8wa_B"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now solve the MPC problem over a simulation horizon $M=25$ from the initial conditions $x_0 = [-4.5, 2]$."
      ],
      "metadata": {
        "id": "vY02VGb9xMP9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "eps = 100\n",
        "\n",
        "w1 = 5\n",
        "w2 = 2\n",
        "w3 = 1\n",
        "w4 = 2\n",
        "w5 = 5\n",
        "\n",
        "P = np.array([[0, 0, 0, 0],\n",
        "              [0, w5, 0, 0],\n",
        "              [0, 0, w4, 0],\n",
        "              [0, 0, 0, w4]])\n",
        "R = w3*np.eye(2)\n",
        "Q = np.array([[0, 0, 0, 0],\n",
        "              [0, w2, 0, 0],\n",
        "              [0, 0, w1, 0],\n",
        "              [0, 0, 0, w1]])\n",
        "\n",
        "Af = np.array([[1, 0, 0, 0],\n",
        "               [0, 1, 0, 0],\n",
        "               [0, 0, 1, 0],\n",
        "               [0, 0, 0, 1],\n",
        "               [-1, 0, 0, 0],\n",
        "               [0, -1, 0, 0],\n",
        "               [0, 0, -1, 0],\n",
        "               [0, 0, 0, -1]])\n",
        "# R = 10*np.array([1]).reshape(1,1)\n",
        "# P = Q\n",
        "N = 5\n",
        "# xL = -5\n",
        "# xU = -xL\n",
        "# uL = -0.5\n",
        "# uU = -uL\n",
        "\n",
        "# States constraints:\n",
        "# xmax = 50000\n",
        "# xmin = 0\n",
        "# hmax = 12000\n",
        "# hmin = 9000\n",
        "# vxmax = 268.54\n",
        "# vxmin = 63.28\n",
        "# vhmax = 15.24\n",
        "# vhmin = -10.16\n",
        "\n",
        "# terminal states\n",
        "xf = 15000\n",
        "hf = 11000\n",
        "vxf = 150\n",
        "vhf = 0\n",
        "\n",
        "hmax = 12000\n",
        "hmin = 9000\n",
        "vxmax = 268.54\n",
        "vxmin = 63.28\n",
        "vhmax = 15.24\n",
        "vhmin = -10.16\n",
        "\n",
        "bf = np.array([xf+eps,\n",
        "               hmax,\n",
        "               vxmax,\n",
        "               vhmax,\n",
        "               -xf+eps,\n",
        "               -hmin,\n",
        "               -vxmin,\n",
        "               -vhmin])\n",
        "\n",
        "# initial states\n",
        "x0 = np.array([0, 11500, 70, 15]).T    # h = 9000~12000 (m)\n",
        "\n",
        "# reference states\n",
        "xref = np.array([0, 11000, 150, 0]).T\n",
        "\n",
        "[model, feas, xOpt, uOpt, JOpt] = solve_cftoc(A, B, P, Q, R, N, x0, xref, Af, bf)\n",
        "\n",
        "fig = plt.figure(figsize=(3, 3))\n",
        "plt.plot(xOpt.T, '-o')\n",
        "plt.legend(['x', 'h', 'vx', 'vh'])\n",
        "plt.ylabel('x')\n",
        "plt.grid()\n",
        "\n",
        "fig = plt.figure(figsize=(10, 2))\n",
        "plt.plot(xOpt.T[:, 0], xOpt.T[:, 1], '-o')\n",
        "plt.legend(['Flight Path (side view)'])\n",
        "plt.axis('equal')\n",
        "plt.ylabel('h')\n",
        "plt.xlabel('x')\n",
        "plt.grid()\n",
        "\n",
        "# print(xOpt.T[:, 0])\n",
        "\n",
        "fig = plt.figure(figsize=(3, 3))\n",
        "plt.plot(uOpt.T, '-o')\n",
        "plt.legend(['ux', 'uh'])\n",
        "plt.ylabel('u')\n",
        "plt.grid()\n",
        "plt.show()\n",
        "# results = pyo.SolverFactory('ipopt').solve(model).write()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 785
        },
        "id": "7LbtUVJXxNJW",
        "outputId": "ce9fe22d-810d-4e3e-a59c-5b47cf4718fe"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 300x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x200 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 300x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import polytope as pt\n",
        "from matplotlib.lines import Line2D\n",
        "\n",
        "nx = np.size(A, 0)\n",
        "nu = np.size(B, 1)\n",
        "\n",
        "# nx = 2, nu = 1\n",
        "\n",
        "M = 80   # Simulation time\n",
        "\n",
        "infeas_flag = False\n",
        "xOpt = np.zeros((nx, M+1))\n",
        "uOpt = np.zeros((nu, M))\n",
        "xOpt[:, 0] = x0.reshape(nx, )\n",
        "\n",
        "xPred = np.zeros((nx, N+1, M))\n",
        "\n",
        "feas = np.zeros((M, ), dtype=bool)\n",
        "\n",
        "fig = plt.figure(figsize=(10, 2))\n",
        "for t in range(M):\n",
        "    [model, feas[t], x, u, J] = solve_cftoc(A, B, P, Q, R, N, xOpt[:, t], xref, Af, bf)\n",
        "\n",
        "    if not feas[t]:\n",
        "        xOpt = []\n",
        "        uOpt = []\n",
        "        infeas_flag = True\n",
        "        break\n",
        "\n",
        "    xOpt[:, t+1] = x[:, 1]\n",
        "    uOpt[:, t] = u[:, 0].reshape(nu, )\n",
        "    line1 = plt.plot(x[0,:], x[1,:], 'b--')\n",
        "    open_loop_line = Line2D([0], [0], linestyle='--', color='b')\n",
        "    # legend_open_loop =plt.legend([open_loop_line], ['Flight Path (side view, open loop)'], loc='upper right')\n",
        "    # plt.legend([open_loop_line], ['Flight Path (side view, open loop)'])\n",
        "\n",
        "\n",
        "#fig = plt.figure(figsize=(10, 2))\n",
        "line2 = plt.plot(xOpt[0, :], xOpt[1, :], 'r-')\n",
        "# plt.xlabel('x(m)')\n",
        "# plt.ylabel('h(m)')\n",
        "# plt.legend(['Flight Path (side view, closed loop)'])\n",
        "# plt.axis('equal')\n",
        "plt.xlabel('x(m)')\n",
        "plt.ylabel('h(m)')\n",
        "closed_loop_line = Line2D([0], [0], linestyle='-', color='r')\n",
        "# legend_closed_loop=plt.legend([closed_loop_line],['Flight Path (side view, closed loop)'], loc='lower right')\n",
        "# plt.legend([closed_loop_line],['Flight Path (side view, closed loop)'])\n",
        "# plt.legend(['Flight Path (side view, open loop)', 'Flight Path (side view, closed loop)'])\n",
        "\n",
        "# Create separate legends for open loop and closed loop\n",
        "legend_open_loop = plt.legend([open_loop_line], ['Flight Path (side view, open loop)'], loc='lower left')\n",
        "legend_closed_loop = plt.legend([closed_loop_line], ['Flight Path (side view, closed loop)'], loc='upper right')\n",
        "\n",
        "# Add the legends to the plot\n",
        "plt.gca().add_artist(legend_open_loop)\n",
        "plt.gca().add_artist(legend_closed_loop)\n",
        "\n",
        "# plt.legend()\n",
        "\n",
        "\n",
        "\n",
        "plt.grid(color='gray', linestyle='--', linewidth=0.5)\n",
        "plt.grid()\n",
        "\n",
        "if infeas_flag:\n",
        "    print(feas) #You may see a plot with some openloop trajectories even when the MPC is not recursively feasible. Ignore this figure.\n",
        "else:\n",
        "    print(feas)\n",
        "    # Plot Closed Loop and Openloop trajectories\n",
        "\n",
        "\n",
        "    fig = plt.figure(figsize=(10, 2))\n",
        "    plt.ylim(60, 270)\n",
        "    line2 = plt.plot(xOpt[0, :], xOpt[2, :], 'r-o')\n",
        "    plt.xlabel('x(m)')\n",
        "    plt.ylabel('vx(m/s)')\n",
        "    plt.legend(['Horizontal Speed'])\n",
        "# plt.axis('equal')\n",
        "    plt.grid()\n",
        "\n",
        "    fig = plt.figure(figsize=(10, 2))\n",
        "    plt.ylim(-11, 16)\n",
        "    line2 = plt.plot(xOpt[0, :], xOpt[3, :], 'g-o')\n",
        "    plt.xlabel('x(m)')\n",
        "    plt.ylabel('vh(m/s)')\n",
        "    plt.legend(['Vertical Speed'])\n",
        "# plt.axis('equal')\n",
        "    plt.grid()\n",
        "\n",
        "# print('ux (horizontal acceleration): ', uOpt[0, :])\n",
        "# print('vx (horizontal speed): ', xOpt[2, :])\n",
        "    fig = plt.figure(figsize=(10, 2))\n",
        "    plt.xlim(0, M)\n",
        "    line3 = plt.plot(uOpt[0, :], '-y*')\n",
        "    line4 = plt.plot(uOpt[1, :], '-ms')\n",
        "    plt.xlabel('M')\n",
        "    plt.ylabel('u')\n",
        "    plt.legend(['ux', 'uh'])\n",
        "    # plt.axis('equal')\n",
        "    plt.grid()\n",
        "\n",
        "    plt.show()\n",
        "\n",
        "# print('Feasibility =', feas)\n",
        "\n"
      ],
      "metadata": {
        "id": "WgLfyrM6xsEs",
        "outputId": "991ddf4c-bcc1-4cf5-ae79-e29e1c55c0dc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ True  True  True  True  True  True  True  True  True  True  True  True\n",
            "  True  True  True  True  True  True  True  True  True  True  True  True\n",
            "  True  True  True  True  True  True  True  True  True  True  True  True\n",
            "  True  True  True  True  True  True  True  True  True  True  True  True\n",
            "  True  True  True  True  True  True  True  True  True  True  True  True\n",
            "  True  True  True  True  True  True  True  True  True  True  True  True\n",
            "  True  True  True  True  True  True  True  True]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x200 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x200 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x200 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x200 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}