{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "ZNsF925iKdjJ" }, "source": [ "# Model Predictive Control of a Double Integrator\n", "\n", "Keywords: model predictive control, cbc usage" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Imports" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "colab": {}, "colab_type": "code", "id": "mcBQgeciKdjK" }, "outputs": [], "source": [ "%matplotlib inline\n", "from itertools import chain\n", "import logging\n", "from mpl_toolkits.mplot3d import Axes3D \n", "import matplotlib.pyplot as plt\n", "import math\n", "import numpy as np\n", "import random\n", "from scipy.interpolate import interp2d\n", "from scipy.integrate import odeint\n", "\n", "import shutil\n", "import sys\n", "import os.path\n", "\n", "if not shutil.which(\"pyomo\"):\n", " !pip install -q pyomo\n", " assert(shutil.which(\"pyomo\"))\n", "\n", "if not (shutil.which(\"cbc\") or os.path.isfile(\"cbc\")):\n", " if \"google.colab\" in sys.modules:\n", " !apt-get install -y -qq coinor-cbc\n", " else:\n", " try:\n", " !conda install -c conda-forge coincbc \n", " except:\n", " pass\n", "\n", "assert(shutil.which(\"cbc\") or os.path.isfile(\"cbc\"))\n", "\n", "from pyomo.environ import *" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "UXgaHTgCKzUu" }, "source": [ "## Model\n", "\n", "The double integrator model is a canonical second order linear system often used to demonstrate control principles. A typical example is Newton's second law where a frictionless mass $m$ is subject to external forces in one dimension\n", "\n", "$$\n", "\\begin{align*}\n", "m \\frac{d^2x}{dt^2} & = f(t) \\\\\n", "\\end{align*}\n", "$$\n", "\n", "where $x$ is position and $f(t)$ is the applied force. It is also reasonably approximates the response of a motor to torque inputs, to a ball moving on a beam that can be tilted, and other mechanical systems. Here we consider a case where the control input $f(t)$ and the position $x(t)$ are both bounded in magnitude.\n", "\n", "$$\n", "\\begin{align*}\n", "| f(t) | & \\leq F \\\\\n", "| x(t) | & \\leq L \\\\\n", "\\end{align*}\n", "$$\n", "\n", "Introducing scaling rules\n", "\n", "$$\n", "\\begin{align*}\n", "y = \\frac{x}{L} \\qquad\n", "u = \\frac{f}{F} \\qquad\n", "\\tau = \\frac{t}{T}\n", "\\end{align*}\n", "$$\n", "\n", "results in the equation\n", "\n", "$$\\frac{m L}{T^2F} \\frac{d^2y}{d\\tau^2} = u$$\n", "\n", "Choosing the time scale $T$ as\n", "\n", "$$T = \\sqrt{\\frac{mL}{F}}$$\n", "\n", "reduces the control problem to a dimensionless form\n", "\n", "$$\n", "\\begin{align*}\n", "\\frac{d^2y}{d\\tau^2} & = u \\\\\n", "\\end{align*}\n", "$$\n", "\n", "subject to constraints\n", "\n", "$$\n", "\\begin{align*}\n", "|u(\\tau)| & \\leq 1 \\qquad \\forall \\tau \\in [0, 1]\\\\\n", "|y(\\tau)| & \\leq 1 \\qquad \\forall \\tau \\in [0, 1]\n", "\\end{align*}\n", "$$\n", "\n", "A variety of control problems that can be formulated from this simple model. Here we consider the problem of determining the range of possible initial conditions $y(0)$ and $\\dot{y}(0)$ that can be steered back to a steady position at the origin (i.e., $y = 0$ and $\\dot{y} = 0$) without violating the constraints on position or applied control action. For the ball-on-beam experiment, this would correspond to finding initial conditions for the position and velocity of the ball that can be steered back to a steady position at the center of the beam without falling off in the meanwhile." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "yB5oS_1xDRkC" }, "source": [ "## Discrete time approximation\n", "\n", "In order to directly construct an optimization model, here we will consider a discrete-time approximation to the double integrator model. We will assume values of $u(\\tau)$ are fixed at discrete points in time $\\tau_k = kh$ where $k = 0, 1, \\ldots, N$ and $h = \\frac{T}{N}$ is the sampling time. The control input is held constant between these sample points.\n", "\n", "Using the notation $x_1 = y$ and $x_2= \\dot{y}$ we have\n", "\n", "$$\n", "\\begin{align*}\n", "\\frac{dx_1}{d\\tau} & = x_2\\\\\n", "\\frac{dx_2}{d\\tau} & = u\n", "\\end{align*}\n", "$$\n", "\n", "Because $u$ is constant between sample instants, integrating the second equation gives\n", "\n", "$$x_2(\\tau_k + h) = x_2(\\tau_k) + h u(\\tau_k)$$\n", "\n", "Substituting and integrating the first equation then yields the pair of equations\n", "\n", "$$\n", "\\begin{align*}\n", "x_1(\\tau_k + h) & = x_1(\\tau_k) + h x_2(\\tau_k) + \\frac{h^2}{2} u(\\tau_k)\\\\\n", "x_2(\\tau_k + h) & = x_2(\\tau_k) + h u(\\tau_k)\n", "\\end{align*}\n", "$$\n", "\n", "This discretization gives\n", "\n", "$$\n", "\\begin{align*}\n", "\\underbrace{\\begin{bmatrix}x_1(\\tau_k+h) \\\\ x_2(\\tau_k+h)\\end{bmatrix}}_{x(\\tau_{k+1})} & = \\underbrace{\\begin{bmatrix}1 & h \\\\ 0 & 1 \\end{bmatrix}}_A \\underbrace{\\begin{bmatrix}x_1(\\tau_k) \\\\ x_2(\\tau_k)\\end{bmatrix}}_{x(\\tau_k)} + \\underbrace{\\begin{bmatrix}\\frac{h^2}{2} \\\\ h \\end{bmatrix}}_B u(\\tau_k) \\\\\n", "y(\\tau_k) & = \\underbrace{\\begin{bmatrix} 1 & 0 \\end{bmatrix}}_C \\underbrace{\\begin{bmatrix}x_1(\\tau_k) \\\\ x_2(\\tau_k)\\end{bmatrix}}_{x(\\tau_k)}\n", "\\end{align*}\n", "$$\n", "\n", "where $y(\\tau_k)$ corresponds to position. The constraints are\n", "\n", "$$\n", "\\begin{align*}\n", "| u(\\tau_k) | & \\leq 1 \\qquad \\forall\\ k=0, 1, \\ldots, N \\\\\n", "| y(\\tau_k) | & \\leq 1 \\qquad \\forall\\ k=0, 1, \\ldots, N\n", "\\end{align*}\n", "$$\n", "\n", "For the purposes here, we will neglect constaints on the dynamics during the periods between sample points. Any issues with intersample dynamics can be addressed by increasing the number of sample points." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "Z-Je8yLjLpHa" }, "source": [ "## Model predictive control\n", "\n", "Given values of the state variables $x_1(\\tau_0)$ and $x_2(\\tau_0)$ and sampling time $h = \\frac{T}{N}$ the computational task is to find a control policy $u(\\tau_k), u(\\tau_{k+1}), \\ldots, u(\\tau_{k+N-1})$ that steers the state to the origin at $t_{k+N}$. The model equations are\n", "\n", "$$\n", "\\begin{align*}\n", "x_1(\\tau_{k+1}) & = x_1(\\tau_k) + h x_2(\\tau_k) + \\frac{h^2}{2} u(\\tau_k)\\\\\n", "x_2(\\tau_{k + 1}) & = x_2(\\tau_k) + h u(\\tau_k) \\\\\n", "y(\\tau_k) & = x_1(\\tau_k)\n", "\\end{align*}\n", "$$\n", "\n", "for $k = 0, 1, \\ldots, N-1$, subject to final conditions\n", "\n", "$$\n", "\\begin{align*}\n", "x_1(\\tau_{k+N}) & = 0 \\\\\n", "x_2(\\tau_{k+N}) & = 0\n", "\\end{align*}\n", "$$\n", "\n", "and path constraints\n", "\n", "$$\n", "\\begin{align*}\n", "|u(\\tau_k)| & \\leq 1 \\qquad \\forall k = 0, 1, 2, \\ldots, N-1 \\\\\n", "|y(\\tau_k)| & \\leq 1 \\qquad \\forall k = 0, 1, 2, \\ldots, N-1\n", "\\end{align*}\n", "$$\n", "\n", "The path constraints need to be recast for the purposes of linear optimization. Here we introduce additional decision variables\n", "\n", "$$\n", "\\begin{align*}\n", "u(\\tau_k) & = u^+(\\tau_k) - u^-(\\tau_k) \\\\\n", "y(\\tau_k) & = y^+(\\tau_k) - y^-(\\tau_k)\n", "\\end{align*}\n", "$$\n", "\n", "where \n", "\n", "$$\n", "\\begin{align*}\n", "0 \\leq u^+(\\tau_k), u^-(\\tau_k) & \\leq 1 \\\\\n", "0 \\leq y^+(\\tau_k), y^-(\\tau_k) & \\leq 1\n", "\\end{align*}\n", "$$\n", "\n", "The objective function is then to minimize\n", "\n", "$$\\min \\sum_{k=0}^N\\gamma \\left[u^+(\\tau_k)+ u^-(\\tau_k)\\right] + (1-\\gamma) \\left[y^+(\\tau_k) + y^-(\\tau_k)\\right]$$\n", "\n", "for a choice of $ 0 < \\gamma < 1$ that represents a desired tradeoff between path constraints on $u(\\tau_k)$ and $y(\\tau_k)$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": {}, "colab_type": "code", "id": "MpxPmXtRVVBF" }, "outputs": [], "source": [ "def mpc_double_integrator(N=2, h=1):\n", " m = ConcreteModel()\n", " m.states = RangeSet(1, 2)\n", " m.k = RangeSet(0, N)\n", " \n", " m.h = Param(initialize=h, mutable=True)\n", " m.ic = Param(m.states, initialize={1:0.5, 2:0.5}, mutable=True)\n", " m.gamma = Param(default=0.5, mutable=True)\n", " \n", " m.x = Var(m.states, m.k)\n", " m.icfix = Constraint(m.states, rule = lambda m, i: m.x[i,0] == m.ic[i])\n", " m.x[1,N].fix(0)\n", " m.x[2,N].fix(0)\n", " \n", " m.u = Var(m.k, bounds=(-1, 1))\n", " m.upos = Var(m.k, bounds=(0, 1))\n", " m.uneg = Var(m.k, bounds=(0, 1))\n", " m.usum = Constraint(m.k, rule = lambda m, k: m.u[k] == m.upos[k] - m.uneg[k]) \n", " \n", " m.y = Var(m.k, bounds=(-1, 1))\n", " m.ypos = Var(m.k, bounds=(0, 1))\n", " m.yneg = Var(m.k, bounds=(0, 1))\n", " m.ysum = Constraint(m.k, rule = lambda m, k: m.y[k] == m.ypos[k] - m.yneg[k])\n", "\n", " m.x1_update = Constraint(m.k, rule = lambda m, k:\n", " m.x[1,k+1] == m.x[1,k] + m.h*m.x[2,k] + m.h**2*m.u[k]/2 if k < N else Constraint.Skip)\n", " m.x2_update = Constraint(m.k, rule = lambda m, k:\n", " m.x[2,k+1] == m.x[2,k] + m.h*m.u[k] if k < N else Constraint.Skip)\n", " m.y_output = Constraint(m.k, rule = lambda m, k: m.y[k] == m.x[1,k])\n", " \n", " m.uobj = m.gamma*sum(m.upos[k] + m.uneg[k] for k in m.k)\n", " m.yobj = (1-m.gamma)*sum(m.ypos[k] + m.yneg[k] for k in m.k)\n", " m.obj = Objective(expr = m.uobj + m.yobj, sense=minimize)\n", " \n", " return m" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "DSeKNks6_OV_" }, "source": [ "## Visualization" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 378 }, "colab_type": "code", "executionInfo": { "elapsed": 1164, "status": "ok", "timestamp": 1555933945959, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg", "userId": "09038942003589296665" }, "user_tz": 240 }, "id": "NZ2OK8Nv_Qae", "outputId": "a1eb7b37-9c99-4388-f659-0e096a6fc395" }, "outputs": [ { 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_results(m):\n", " results = SolverFactory('cbc').solve(m)\n", " if str(results.solver.termination_condition) != \"optimal\":\n", " print(results.solver.termination_condition)\n", " return\n", " \n", " # solution data at sample times\n", " h = m.h()\n", " K = np.array([k for k in m.k]) \n", " u = [m.u[k]() for k in K]\n", " y = [m.y[k]() for k in K]\n", " v = [m.x[2,k]() for k in K]\n", " \n", " # interpolate between sample times\n", " t = np.linspace(0, h) \n", " tp = [_ for _ in chain.from_iterable(k*h + t for k in K[:-1])]\n", " up = [_ for _ in chain.from_iterable(u[k] + t*0 for k in K[:-1])]\n", " yp = [_ for _ in chain.from_iterable(y[k] + t*(v[k] + t*u[k]/2) for k in K[:-1])]\n", " vp = [_ for _ in chain.from_iterable(v[k] + t*u[k] for k in K[:-1])]\n", "\n", " fig = plt.figure(figsize=(10,5))\n", " \n", " ax1 = fig.add_subplot(3, 2, 1)\n", " ax1.plot(tp, yp, 'r--', h*K, y, 'bo')\n", " ax1.set_title('position')\n", "\n", " ax2 = fig.add_subplot(3, 2, 3)\n", " ax2.plot(tp, vp, 'r--', h*K, v, 'bo')\n", " ax2.set_title('velocity')\n", "\n", " ax3 = fig.add_subplot(3, 2, 5)\n", " ax3.plot(np.append(tp, K[-1]*h), np.append(up, u[-1]), 'r--', h*K, u, 'bo')\n", " ax3.set_title('control force u[0] = {0:<6.3f}'.format(u[0]))\n", "\n", " ax4 = fig.add_subplot(1, 2, 2)\n", " ax4.plot(yp, vp, 'r--', y, v, 'bo')\n", " ax4.set_xlim([-1.1, 1.1])\n", " ax4.set_aspect('equal', 'box')\n", " ax4.set_title('phase plane')\n", " ax4.set_xlabel('position')\n", " ax4.set_ylabel('velocity')\n", " \n", " for ax in [ax1, ax2, ax3, ax4]:\n", " ax.set_ylim(-1.1, 1.1)\n", " ax.grid(True)\n", " fig.tight_layout()\n", "\n", "model = mpc_double_integrator(5, 0.5)\n", "model.ic[1] = 1.0\n", "model.ic[2] = 0.2\n", "\n", "SolverFactory('cbc').solve(model)\n", "plot_results(model)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "qBFnxTiH8T0Y" }, "source": [ "## Interactive use" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "fvUUUa3t8eC1" }, "source": [ "### Google Colaboratory\n", "\n", "When run in Google Colaboratory, the following cell opens a GUI form that can be used interact with the model described above." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "cellView": "both", "colab": { "base_uri": "https://localhost:8080/", "height": 378 }, "colab_type": "code", "executionInfo": { "elapsed": 1824, "status": "ok", "timestamp": 1555933160138, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg", "userId": "09038942003589296665" }, "user_tz": 240 }, "id": "pbbkvpB7fWLH", "outputId": "5e74aed9-ea27-4de8-cc02-568dd53b9d3b" }, "outputs": [ { "data": { "image/png": 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Y5+4fA5jZdOA44N1Gjj8d+FGaYhMRyRpKjiU7LF8O//kPfOUrYfuoo+CDD2DUKDj+ePL+8iVly3s3OE3Tq0kHMgJYkLC9ENgv2YFmlg+MAWYl7O5hZq8BVcCt7v54I+cWAoUAQ4cOpbS0tNWBVlRUtOm8VFMciiMb4oDMiaWjxKHkWDLTl1/CP/9Z2zv8xhvQv394uK5zZyguDjNKjB0LZkwt0bLA0uElG0DvjRx7GvCou29K2Jfn7ovNbFtglpm97e4fNbigezFQDDBhwgRvy0IqpaWlGbEAi+JQHNkQB2ROLB0lDs1WIZmhujrMHrFhQ9i+/nqYMgXuuCMsxXzjjWH6tZoH6A46CHbYYfN2QUHIl/Pzw678/LCtWSSkA1kIjErYHgksbuTY04AHE3e4++Lo/WOglLrjkUVEOgz1HEu7KSmpmQv4YPLyaDgX8Cef1PYMP/ssrFwJpaVw8MFw7rnh/aCDQnLcAulehlgkw7wKjDWzMcAiQgJ8Rv2DzGxHYADwUsK+AUClu683s0HAgcBP0xK1iEiGUXIs7aLu1GoWplb7lsOaNRRc3B9efhkOOCAcPGIEHHtsmFFi993Dvp13Di8RaRF3rzKzS4GnCFO53ePu75jZjcBr7j4jOvR0YLq7Jw652BmYZmbVhG8Ub02c5UJEpCNRciztoqio7vhfgMovjaKrqym4mDCt2p13hoR4xx0137BICrj7TGBmvX3X1du+Psl5LwK7t2twIiJZQsmxpE51NXz2GQwfTnm5k+z5oPKKAeFD165w6aXpjU9ERESkGXogT7bMwoXw+9/DGWfA8OFhjDCQl5e8J7ix/SIiIiKZICuS45ISGD0aJk8+mNGjw7bE5IsvoGao4ve/H+YZPu88mDUrzC5x7bVQXc3UqWEqtUSaWk1EREQyXcYPq0j6YFdhKNPMBGmwcSP8619hRomnn4ZXXoE334RddoHDDw/LME+ZArvtVmfccM3PJsxW4eTlWcPZKkREREQyTMYnx0kf7KoM+5VotQN3qKoKY4JfegkOOyz0FpvBhAlw1VW1U6tNmhRejaiZWq209LmMmDRcREREpDkZP6yivLyx/V779b60WM0QlU6dqB2isnQpPPhgGB6Rnw8/+1k4eOedw1jiRx8Nyzf/619hXITWZBYREZEclfE9x3l5UFaWZL+XwfgTQ+9m9+7pDywLldRbYrmsDArP/hKqL6eAB2HAAJg8OQyRgLBc829+E1/AIiIiImmW8T3HSR/s6ulMPe8j2G+/2sT4llvgscdg/fr0B5np1q+HF16g6JLVDYeoVPekqP//hl7hZctCL/FRR8UTp4iIiEjMMr7nOPmDXUZBwdeBr4fCdevg178O04oNGADHHAMnngiHHgo9e8YWe2w2bIBu3cLnH/4QbrsN1q2jnE1JDy9f0w/22SeNAYqIiIhkpozvOYaQIM+fD7NmPcf8+UkexOvRAz75BGbOhKOPhhkz4PjjwwpsAGvXwqJFaY46TdxD2x98EC6/PCzJ3LdvGEcMYdzwhRfCY4+RNzL5GG0NIRYREREJsiI5bpEuXeCII+C++0Ji+Pe/h4fJAJ54AkaOhF13DQnkX/8KK1cmvUzSB9baUavmcHYPA4VnzKhN9u+/H7bdNrS1uDjMMnHZZWHGCQj777gDjj+eqbd21tzDIiIiIk3YomEVZnYycD2wM7Cvu7+WiqC2WNeuYe7dGvvuC//zPyFhnjYNfvGLsL+8PCxi8e67sG4dJW/uRuGl3eo+sNaOcyo3OYfz6dUhQ1+yBH7yE5g7N8wvvHp1OOCee+Cb34SJE+F//xf23z88SNel8R9p3SEqocdYcw+LiIiI1NrSnuN/AycCz6cglvYzejRceWVIjleuDKu53XZb6E2G8DDf+PEUnbck+ZzK11RDdXXKw2p0DuezF8DNN4cdXbrA3XeHh+pOPTUkwi++CKecEspHjQrDJsaNazIxrlEzRKW6muRDVEREREQ6sC3qOXb39wAsYWW0jNezZ8PFK264AY49lvJTkg++LV8QnTdsGAwaBIMHw/jxteMRfvMbWLMmjH02C0Ma8vPhpJNC+bXXhmEQq1fDqlXw6acwZQrl5Xcmr696JOy1V9gYPBg+/zz0IouIiIhIu0rbbBVmVggUAgwdOpTS0tJWX6OioqJN57XI4MEMGbqezz7r0aBoWL81lB9xIt1WrqTrmjV0LSvjy02beC+KZd+bb6bXggV1zlmx7768vfXWAEx44AG6rF1LVZ8+VPXuzYZhw1jVtStDhqxLWt+Qoesp7d0b2qutadauP7eY5XLbILfbl8ttExGRtms2OTazZ4BhSYqK3P3/WlqRuxcDxQATJkzwtiwnXFpa2q7LEN9+e91FMiA8sPY/dw0gr+DBOsf2BYbWbMyfH6aTW7cubHfpwtbdujGxR5T4fvxxg7qGALePT17f7bf3yKnlltv75xanXG4b5Hb7crltIiLSds0mx+5+SDoCyQRtfmCtU6eQ1dafCqJV9dXM4axxwCIiIiJxiWURkDlz5iw3sySLQjdrELA81fE0pqwMzjwzvNJgUFkZy9NYXzql9eeWZrncNsjt9rW1bfmpDkRERDLHlk7ldgJwJzAYeMLM5rr7Yc2d5+6D21jfa+4+oS3nZjq1LTvlctsgt9uXy20TEZG229LZKh4DHktRLCIiIiIisdL8YCIiIiIikWxLjovjDqAdqW3ZKZfbBrndvlxum4iItFFWJcfRdHA5SW3LTrncNsjt9uVy20REpO2yKjkWEREREWlPSo5FRERERCJZkRyb2eFm9oGZzTOzq+OOJ5XM7B4zW2pm/447llQzs1FmNtvM3jOzd8zsO3HHlCpm1sPM/mVmb0ZtuyHumFLNzDqb2Rtm9te4Y0klM5tvZm+b2Vwzey3ueFKtufulmZ1rZsui9s81swsSys4xsw+j1znpjVxEJDPEsghIa5hZZ+AuYAqwEHjVzGa4+7vxRpYy9wK/Au6LOY72UAV8191fN7OtgDlm9nSO/OzWA5PdvcLMugIvmNnf3P3luANLoe8A7xFWS881k9w95xY3acX98iF3v7TeuQOBHwETACf8e53h7qvSELqISMbIhp7jfYF57v6xu28ApgPHxRxTyrj788DKuONoD+6+xN1fjz5/QUi0RsQbVWp4UBFtdo1eHmNIKWVmI4GjgLvjjkVaZUvul4cBT7v7yighfho4vJ3iFBHJWBnfc0xIphYkbC8E9ospFmkjMxsN7AW8Em8kqRP10s0BtgfucvecaRvwc+AqYKu4A2kHDvzdzByYlmOzVrT0fnmSmR0E/Ae4wt0XNHJug19mzawQKAQYOnQopaWlrQ6yoqKiTeelmuJQHNkQB2ROLB0ljmxIji3JvpzpoesIzKwP8Cfgcnf/PO54UsXdNwHjzKw/8JiZ7ebuWT923MyOBpa6+xwzmxh3PO3gQHdfbGZDgKfN7P3oG5xc0JL75V+AB919vZldCPwBmNzCc2umwCsGmDBhgk+cOLHVQZaWltKW81JNcSiObIgDMieWjhJHNgyrWAiMStgeCSyOKRZppWg87p+AEnf/c9zxtAd3Xw2UkjtfQR8IHGtm8wlfy082s/vjDSl13H1x9L4UeIwwFCFXNHu/dPcV7r4+2vwtML6l54qIdATZkBy/Cow1szFm1g04DZgRc0zSAmZmwO+A99z9Z3HHk0pmNjjqMcbMegKHAO/HG1VquPs17j7S3UcT/r3NcvczYw4rJcysd/RwKGbWGzgUyPre/gTN3i/NbHjC5rGEZwEAngIONbMBZjaA8GfzVBpiTrmSEhg9Gjp1Cu8lJR2n/o7cdpFUyfhhFe5eZWaXEm7SnYF73P2dmMNKGTN7EJgIDDKzhcCP3P138UaVMgcCZwFvm9ncaN8P3H1mjDGlynDgD9G4407Aw+6eU1Oe5aihhCEwEO5/D7j7k/GGlDqN3S/N7EbgNXefAfyXmR1LmE1mJXBudO5KM/sxIcEGuNHds+5h4ZISKCyEysqwXVYGhYUOmzZRcFZnMINNm6C6Gquqgo0ba0/u2jW8V1WBJxm914LyUL9TWWkN6z+7S9Lzraoq7OsSlSfGtPkga7a85KEujbf9DJo+v1PUV+YeYklW3rlzk+Ul0zsnaXsoLihoeIpIxnJ3vfTSSy+99Gr1a/z48d4Ws2fPbtN5LZGf7x4yuLqvfD5x/+KLcNAVVyQ/qMa3vtWwbKutastPO61h+fDhTdffZWHt+Qcd1PCAxD/LvfZqWD5xYm352LENy485pum2n3567fm9ezc8qLAw/Fyqq5Nf5LvfDeeuWZO8/PrrG68/v3U/w/b8+9EamRKHe+bEku1xEDoJmr23ZXzPsYiISEuVlzeyn3zoFvWYHnEEbL01H3/yCduOGdPw4OOPh/z8uvu6dav9fMopsNtudcv79Gm6/qptajcuuAAOPXTz5seffMK2BxxQW37JJfDpp3UvkBjPFVfAynqd+mPHUn5aI3WTH2Kucd11DXuP99qr9vNNNzW8yH7RpCfduycv/9rXKG9kKaTG/kxEMpWSYxERyRl5eeHr/Ab78602wZ0yBaZMoby0lG2TPfF+5JHh1ZgTTgiv1tZf46yz6pQ1iOP88xuvG+Cii5LXfVUTdR9/fO2Oq65Kft3S0jB8o6io8bq7d2+0vNG25zV+OZFMlA0P5ImIiDTvJz9hauF8evWqu7tXL5g6NT0hTJ1KbPXHWXcm1C+SKkqORUQk+91wA1x9NQXLf0lxcRiFYBbei4vT90BYQQGx1R9n3Q3qx8lnPsXXLdDDeJJ1NKxCRESy2003wfXXw7nnwm23UdAp3tkRCgriqz/OuuvUv7YS3l0G++wTXzAibaSeYxERyV533gk//CGcfTbcfXftlGQSr969lRhL1tJdREREslN1Nfztb+Fhs9/9LszDK5nDHS68EP77v+OORKRVlByLiEj2cQ+9xI8/Dg8+WLvAhWQOM9iwAaZNg1Wr4o5GpMWUHIuISHZ56SWYNAmWLQvTs/XoEXdE0pjLLw9L9v32t3FHItJiSo5FRCR7zJsHRx8NixaFYRWS2fbYAyZPDmPDky07LZKBlByLiEh2WLUKjjoqfF3/5JMwdGjcEUlLXHYZLFwIM2fGHYlIi2iQloiIZL6NG+Eb34BPPoFnn4Xttos7Immpo48OM4rsvnvckYi0iHqOJauY2blm9sIWXuNrZvZBqmISkTRYtiz0Pt59N3zta3FHI63RpQvceCOMGRN3JCItop5j6XDc/R/AjjXbZjYfuMDdn4ktKBFp2jbbwJtv6uG7bPbMM2FozMknxx2JSJPUcywiIpnrhRfgggvCjAdKjLPb7bfDFVfApk1xRyLSJCXHEgszu9rMHq237xdm9ksz62dmvzOzJWa2yMxuMrOks/ub2VfM7FUzWxO9fyWhbKCZ/d7MFpvZKjN7PNo/0cwWRp//COQBfzGzCjO7ysyeMLPL6tXzlpkdn+o/BxFpwqefwimnwHPPhTHHkt3OPz/MMjJrVtyRiDRJybHE5UHgSDPrCxAlv6cADwB/AKqA7YG9gEOBC+pfwMwGAk8AvwS2Bn4GPGFmW0eH/BHoBewKDAHuqH8Ndz8LKAeOcfc+7v7TqP4zE+rZExgB6FFrkXSpqoLTToPVq+FPf4J+/eKOSLbU0UeHn+P998cdiUiTlBxLLNy9DHgdqOmNnQxUAp8ARwCXu/tad19KSGpPS3KZo4AP3f2P7l7l7g8C7wPHmNnw6DoXuvsqd9/o7s+1MLz/A8aa2dho+yzgIXff0IamikhbFBWFHuNp08JcuZL9evQIM478+c9hmIxIhlJyLHF6ADg9+nxGtJ0PdAWWmNlqM1sNTCP0/Na3DVBWb18ZoZd3FLDS3Vu9Zqm7rwceBs40s05RjH9s7XVEpI2WLw9J8be/DWedFXc0kkoFBaH3+MMP445EpFGarULi9Ahwu5mNBE4ADgBWA+uBQe7e3HJKiwnJdKI84ElgATDQzPq7++pmruNJ9v2BkBC/AFS6+0vNXENEUmXQIJg7F4Yk+51YstrBB0NZGXRO+hiJSEZQz7HExt2XAaXA74FP3P09d18C/J2QNPc1s05mtp2ZHZzkEjOBHczsDDPrYmanArt6rp1zAAAgAElEQVQAf42u8zfg12Y2wMy6mtlBjYTyGbBtvdheAqqB21GvsUh6uIeV79xh9Gjo1SvuiCTVOnUKiXF1tR6ylIyl5Fji9gBwSPRe42ygG/AusAp4FBhe/0R3XwEcDXwXWAFcBRzt7sujQ84CNhLGIS8FLm8khluAa6NhHFcm7L8P2B3Q0yMi6XD//XDEEfDQQ3FHIu3pk0/CvNWPPBJ3JCJJaViFxMrd/0i9nll3XwNcFL3qH38vcG/C9gvA+EauvRI4J8n+UmBkwvb/ER7Cq68c+Ke7f9xsQ0RkyyxZApddBl/9qhaJyHX5+WAGjz0GZ5wRdzQiDajnWCQJM+sFXAwUxx2LSIdw2WWwbh3cc4/Go+a6Tp3g+OPhb3+DL7+MOxqRBpQci9RjZocBywhjkR9o5nAR2VKPPx7mMv7Rj2Ds2OaPl+x3wgmwdm1YUlokwyg5FqnH3Z9y997uflwLZswQyRhmdriZfWBm88zs6iTl/21m70YrPj5rZvkJZZvMbG70mpHWwHv3DgtEXHll88dKbpg4Efr2hRnp/asm0hIacywikgOiVSbvAqYAC4FXzWyGu7+bcNgbwAR3rzSzi4CfAqdGZV+6+7i0Bl1jypTwko6jWze4/XbYbru4IxFpICXJsZndQ5g1YKm779bc8YMGDfLRo0e3up61a9fSu3fv1geYBdS27JTLbYPcbl9b2zZnzpzl7j64HULaUvsC82oeIDWz6cBxhFlfAHD32QnHv0zCMunp9MwzQzj3XCgvd/L6rmHqHT0p+Gb3OEKROF1wQdwRiCRl7snWP2jlRcL8sRXAfS1JjidMmOCvvfZaq+spLS1l4sSJrQ8wC6ht2SmX2wa53b62ts3M5rj7hNRHtGXM7BvA4e5+QbR9FrCfu1/ayPG/Aj5195ui7SpgLlAF3OrujzdyXiFQCDB06NDx06dPb1WczzwzhNtu24H162v7Zrp3q+LK7/2HQw5Z2qprbamKigr69OmT1joVRwJ3+r73Hg58scsu8cXRiEyJAzInlmyPY9KkSS26f6ek59jdnzez0am4loiItIkl2Ze098PMzgQmAImL6+S5+2Iz2xaYZWZvu/tHDS7oXkw0i8uECRO8tb9gnHsurF9fd9/6DV24//5duOmmXZKe014y5Ze/Dh3Ht78dHsK8+OJ440giU+KAzImlo8SRtjHH9XobKC0tbfU1Kioq2nReNlDbslMutw1yu3052LaFwKiE7ZGEJdbrMLNDgCLgYHffnKa6++Lo/WMzKwX2Ahokx1uqvLx1+yXHTZkC994bVsvr2jXuaESANCbHW9rbAJnzG0t7UNuyUy63DXK7fTnYtleBsWY2BlgEnAbUWWHBzPYCphGGXyxN2D8AqHT39WY2CDiQ8LBeyuXlQVlZ8v3SAR18MPz61zB3LuyzT9zRiACayk1EJCdE0w5eCjwFvAc87O7vmNmNZnZsdNj/AH2AR+pN2bYz8JqZvQnMJow5fpd2MHUqdO++qc6+Xr3CfumADjwwvL/wQrxxiCTQVG4iIjnC3WcCM+vtuy7h8yGNnPcisHv7RhcUFMB7733A/ffvQnl56DGeOjXslw5oxAgYMwb++U+44oq4oxEBUjeV24PARGCQmS0EfuTuv0vFtUVEJLcc8vXP0v7wnWSwJ5+EUaOaP04kTVIyrMLdT3f34e7e1d1HKjEWEZHGbDttGuy5J6RgKlHJATvsAD17xh2FyGYacywiImnV9/33oUcPsGSzz0mHs2YNfP/7kFuzx0gWU3IsIiLpU11Nnw8/hAkZt46KxKVnT7jjDvjb3+KORARQciwiIulUVkaXykoYNy7uSCRTdOsGu+8Ob7wRdyQigJJjERFJp/ffD+877xxvHJJZ9toLXn9d49AlIyg5FhGR9Bk6lMVHHQW7aLYKSbD33rBiBSxcGHckIkqORUQkjfbem/9ceSUMHBh3JJJJdt0Vtt4aFjdY8Vwk7ZQci4hI+ixZAtXVcUchmeagg2D5cthvv7gjEVFyLCIiabTnnuzw85/HHYVkGk3rJxlEybGIiKTH2rWwbBnrhg2LOxLJRNddBxdfHHcUIkqOO5qSEhg9Gjp1Cu8lJe1f1+TJB7d7XYn15WLbRHLCggUArBsyJOZAJCPNnw9/+UvcUYjQJe4AJH1KSqCwECorw3ZZGRQWOlRVUXBavTGA3bqFr7mqqmDTpoYXqynfuDHp+MGSR7sn1GUN6+rePRzYyPmbyzdsaDi1j1moP6G8ZHonCi/uQmWlJbSNqL5NjZ+/fn3Dujt1gq5dGy0veagzhRd1qde2UFZQ0PByIvWZ2W3A7939nbhjSavycgDWDx0acyCSkbbdFu6/H9u4Me5IpINTz3FHUFkJTz9N0cWrNifGtUVG0bmLwlKuia9Vq8IB117bsKxHj5A0A1xxRcOyfv0oKqLxukaMqN156qkNz99pp9ryo45qWJ64stZBB0GPHhSdu2hzYpzY7KJvLW14/rHH1h60ww4Ny08/vbZ8+PAG5UUXr07SNigqasHPQiR4Hyg2s1fM7EIz6xd3QGlRVgao51gaMXIkuNN9xYq4I5EOTj3HuWj9+tAb27MnzJgB3/gGbNxIOUl6gIFy8uHmm+vu7NkzvB92GPRL8v92p+j3qmOPrZvsAnTuTPnVyUMrJz8k3DUKCmCffeoelFjfeefB5Ml1ywcPrv180UVw3HGU/yA/eX0bhzds27bb1n6+6ir4/PO65TvuWPv5hz+EdevqXrNo6+R1lTms31Db6y3SCHe/G7jbzHYEvgm8ZWb/BH7r7rPjja4d7bMP3HQTGwYNijsSyUSjRgHQfdmymAORjk7JcS6oqoI5c2DWrPD65z/hzjvh/PNhzz1D7+7kyeR9C8oWNDw9L9/gmmuSX3vSpPBqzKGHhlf9a/56cydRw7ouv7x2x0knNd22xF7cZM45J1x3WhP1NdY2gEsuafr6V1zR8JqN1UUZ7DgRXngh9ICINMHMOgM7Ra/lwJvAf5vZt939tFiDay/jxsG4cXhpadyRSCYaMyaslKep/iRmGlaRjaqrYeXK8Pnzz8PE6fvvDz/4AXz2WRgAu+eeoTw/H37yEzjsMKbe0olevepeqlcvmDo19SFOnUra6kp3fY3WdfUXMGVKbU/6Rx9pKVRJysx+RhhacSRws7uPd/efuPsxwF7xRteO5s2DRYvijkIy1Q47wOuvs6bm/y+RmCg5zgbu8P778OtfhyESQ4bAN78Zyvr2DT2xDz0UEuO33oKf/7zuuNxIQQEUF4d82Sy8Fxe3z0Nkdevydq2rYX0xte2W3eG3vw0BLF0aeskmToSXX059EJLt/g3s6e7fdvd/1SvbN46A0uLsszd/2yMikqmUHMes0SnBPvus9qBjjoGddw5DAP71r7B91lm15TfcAKecEpLmZhQUhNlyqqvDe3vOrlBT16xZz7V7XYn1ZUTb+vcPPfYffAAHHAAnnhh+wREJCty9zmOdZvYsgLuviSekNFixInzTJdKYo49m22nT4o5COjglxzGqmVqtrAzcoynBzllPyeDvhG7JmgfBzjordE3OmxcO/v3vQw+yZK5u3cJk9vPmwY03wjPPwO67b57nVTomM+thZgOBQWY2wMwGRq/RwDbxRpcGy5eDHsaTpixcSK9oyj+RuOiBvBglne5sU3eK1hZRcNvY2unSTj01/cFJavTpE2a8uPBCeOKJzU9j88gjcMghMGBAvPFJun0buJyQCL+esP9z4K5YIkqXTZvCFJHqOZamDBxIl+XL445COjj1HMfl008pL0/+sFb5uiFw6aUhsZLcMHgwnHtu+Lx4MZxxBmy3Hdx2W4Op4iR3ufsv3H0McKW7j0l47enuv4o7vnZVWRmen+jbN+5IJJNtvTVd60+vKZJmSo7TbcMGuP122GEH8rp9lvSQvLw0xyTptc028OqrsN9+8L3vwdixYahMspUIJaeYWc2k3YvM7MT6r1iDa2/dusEf/gCHHx53JJLJ+vWjy9q1cUchHZyS43R68knYYw+48ko4+GCmTvW0TncmGWTcOPjb38K81MOHh/HJn34ad1TS/g6O3o9J8jo6rqDSonv3MFvFbrvFHYlksj32YPUee8QdhXRwGnOcLg88EKY0GDs2jD098kgKAIaFscfl5U5enjF1avvP6iAZZNIkeOUVeOedMD+ye/jl6cQT4cAD445OUszdfxS9fzPuWNJu7Vp44w3YZZe4I5FM9l//xXt77MHQuOOQDi0lPcdmdriZfWBm88yskYWDO6AvvoC33w6fTzghrFr373/DkUduPiTd051JBjKr7U1bsiT8IvXVr8Jxx4WkWXKOmd1sZv0TtgeY2U0punaT92Mz625mD0Xlr0QzZdSUXRPt/8DMDktFPJt98AF87Wvw/PMpvayISKptcXIcLYF6F3AEsAtwupl17K6B6mr44x9hxx1DUlxVBT17hofsunWLOzrJZNtsE6Z/mzoVSkvDMJzzzqNk2heMHg2dOlF3Pux20uj82+1YVy62rQlHuPvqmg13X0VYLW+LtPB+fD6wyt23B+4AfhKduwtwGrArcDjw6+h6qbF+fXjv0SNll5TcsuuuYWGlSZMOxszZdde4I5KOKhXDKvYF5rn7xwBmNh04Dng3BdfOPq+9Bv/1X/DSS7DPPqG3uItGr0gr9O4dlgIvLIRbbqHkDxspnN6Hyi9DcVkZFF6wCeYvoODIVWE6uNGjQ+HcuQ2XrB40KEwh5x7K6xsyJAzpqKqCt9+mZOYACm8aReW6zkA0/3YhUFVFwR5vNzx/xIhwjS+/TL7QSV5emL5r7Vr4z3/qFJXMHEDh1Hwqv7TkbYMwq0ffvrB6NXzyScPrjx0bZnZZuTJcoL6ddgq/nC5bRknx2uRtI+3f2nQ2s+7uvh7AzHoC3VNw3Zbcj48Dro8+Pwr8ysws2j89iukTM5sXXe+lFMQl0qRdd4V33wWwzfvefTfs1xdokm6pyNpGAIkrGywE9kvBdbPPSy+FcaJDhoTZB84+O3SHibTFoEFw++0UPepUrrA6RZXrOlN0LRRcuzeceWb4pgLCanz1p4a76KKw9PimTbD33g3rueqqsJrfF1/A3ntTxCdUUrfDsLIyjI0vWJTk/J//HL7znZC4Jrv+3XfD+eeHIUX771+nKNTVRNsAZs6EI46A2bPDWOz6/vGPMAzliSfCv7n65s6FPfeERx6h6NojG29bepPj+4Fnzez3gAPnAX9IwXVbcj/efIy7V5nZGmDraP/L9c4dkYKYAot+zvV/eROhJjFu+X6R9mS+hTcqMzsZOMzdL4i2zwL2dffL6h1XCBQCDB06dPz06dNbXVdFRQV9MmzuX6uqovfHH1Oxww5QXc2IP/+ZT484gk29e7fqOpnYtlRR27bM5MkH424N9hvOmz+eyvrBg6nYcUcAtn7xxTCsJ8G6YcNYu/32UF0dyuv5csQIKseMwTZuZOArr7DnD4twktRnzps3NpxKZe2YMawbMYLOlZX0f/31BuUV22/P+mHD6PLFF/R78806ZY3WFbUN4PNddmHjwIF0W7GCrd57r8Gxa3bfnap+/ei+dCl96vVMA6weN45NffrQY8kSvnLGaY22bdas5xrsT2bSpElz3H1Ciw5ugpkdDhwSbT7t7k+l4JrN3o/N7J3omIXR9keEHuIbgZfc/f5o/++Ame7+p3p1tOlevtW77zL+kkt465ZbKN9tt4y4J2TKvUlxwKRJB0OSf5vgzJ7dsn+bqZYpPxfInFiyPY4W37/dfYtewAHAUwnb1wDXNHXO+PHjvS1mz57dpvPazVNPue+0k3vfvu4rVmzRpTKubSmktm2Z/Hz30N1W95Wfn/31ZWPbgNd8C++b4TIMpXYKtyEpumaz92PgKeCA6HMXYDkhK6lzbOJxjb1adS9fscL90UfdlyzJmHuC4qgrzjiS/busecUlU34u7pkTS7bH0dL7dyq+838VGGtmY8ysG+GBjhkpuG7m+uijMJPAYYfBxo3hiR4tAyztZOpU0jofdjrry+W2NcXMTgH+BXwDOAV4xcy+kYJLt+R+PAM4J/r8DWBW9J/GDOC0aDaLMcDYKMbUGDgQTjoJhg1L2SUldzQ2w59m/pM4bPGYYw9j1i4l9DJ0Bu5x99wdPr9gQXhCoEsXuOUWuOKKMLm9SDupGQsb5sMOz7e153zYdetr3/m3c7ltzSgC9nH3pQBmNhh4hvCAXJs1dj82sxsJPSYzgN8Bf4weuFtJSKCJjnuY8PBeFXCJu6du2ca1a+Gf/0RTEEgy77yT+FCeA8Yuu+hhPIlHSqZRcPeZwMxUXCsjucPrr8P48eGp/zvuCD3H22wTd2TSQRQUpDeBq6mvtPQ5Jk6cmJa60iWdbWtCp5rEOLKCFM07n+x+7O7XJXxeB5zcyLlTgfbpR//ss/Bt2733Qn5+u1Qh2a0mEY7536aIlo+ur8Gcq1Pnh4nr99uvdpqqiy5SYiwiW+JJM3vKzM41s3OBJ8jlDgYI0+0BVFTEG4eISDM0AW+CkpIw52llZdguK4PCawfDVrtR8Jtzw3yqIiJbyN2/Z2YnAQcSHoYrdvfHYg6rfdXM4LN2bbxxiIg0Q8lxgqKi2sS4RiW9Kep3FwUXpG6hKBERD1Ok/anZA3NFz55hrmP1HItIhlNynKC8PDwE0GD/IiXGIrLlzOwLwtNGDYoIc1b1TXNI6dOpU+g9/uKLuCMREWmSkmOA+fPhu98lz2+njNENivPy0h6RiOQgd98q7hhi9fjj4WGOBQuaPVREJC4d+4G8ykq47jrYeWd48kmmnjyXXr3qdurEMQeqiOQ+M/uqmX0z+jwomls4t33967DddnFHISLSpI6bHLvDQQfBj38MJ54IH3xAwcPHU1xs5OeHoXH5+VBcHMscqCKSw8zsR8D3CavSAXQD7o8vojR59VV4LLefOxSR7NfxhlW88w7suGNYxOOHP4Stt4avfnVzcbrnXBWRDukEYC/gdQB3X2xmuT/kYto0mDkTHngg7khERBrVcXqOV6yAiy+GPfaAu+8O+447rk5iLCKSJhuiJZsdwMx6xxxPegwZAsuWQXV13JGIiDQq95Pjqiq4664wR3FxMVx6KZx6atxRiUjH9rCZTQP6m9m3CEtH/zbmmNrf8OFQVUXX1avjjkREpFG5P6yioAAefhgmT4Zf/AJ22y3uiEREqoF/AJ8DOwDXufvT8YaUBqNHA9Dj00/jjUNEpAm5mRyXlcGAAdC3b21P8QknhKfsRETitxVwPrASmA68FW84aTImTMjRU8mxiGSw3BpWUVkJ118PO+1UO//a174WZqNQYiwiGcLdb3D3XYFLgG2A58zsmZjDan877ACvv87yAw6IOxIRkUblRnLsDo8+GuYrvuEGOPZYuOSSuKMSEWnOUuBTYAUwJOZY2l+3brDXXlT37Bl3JCIijcqN5Pjaa+Hkk6F/fygthYce0rJ2IpKxzOwiMysFngUGAd9y9z3ijSpNZsxg2MyZcUchItKo7B1zvHIlrF8fnn4+6ywYMQIKC8P8xSIimS0fuNzd58YdSNo98gijn3oKfvrTuCMREUkqK3qOS0rCQ86TJx/M6Hyn5Lxnwti1yy4LB+y0U5jDWImxiGQBd7+6QybGALvuSo9ly0DTuYlIhsr45LikJHQIl5WBu1FWbhT+/gBKBn8Hrrsu7vBERKQ1dt01vL/7brxxiIg0IuOT46KiMAlFokp6U1R5bVjtTkREskdNcvzOO/HGISLSiIxPjsvLG9m/QFOziYhkndGj2dSjB8ybF3ckIiJJZXxy3NikE5qMQkQkC3XqxEsPPQS33hp3JCIiSWV8cjx1KvTqVXdfr161a3yIiEh2qerbVwsziUjGyvjkuKAAioshPx/MnPz8sF1QEHdkIiLSFr3mz4fTT9fQChHJSBmfHENIhOfPh1mznmP+fCXGIiJZb/p0ePHFuKMQEWlgi5JjMzvZzN4xs2ozm5CqoEREJHdVjhoFffrAq6/GHYqISANb2nP8b+BE4PkUxCIiIh1B584wfjy88krckYiINLBFybG7v+fuH6QqGBERaRszG2hmT5vZh9H7gCTHjDOzl6Jv/N4ys1MTyu41s0/MbG70GteuAR94ILzxBlRUtGs1IiKtlbb1ls2sECgEGDp0KKWlpa2+RkVFRZvOywZqW3bK5bZBbrcvB9t2NfCsu99qZldH29+vd0wlcLa7f2hm2wBzzOwpd69Zy/l77v5oOoItqT6NIruE8r69ycsLMxDpeRIRyQTNJsdm9gwwLElRkbv/X0srcvdioBhgwoQJPnHixJaeullpaSltOS8bqG3ZKZfbBrndvhxs23HAxOjzH4BS6iXH7v6fhM+LzWwpMBhYTRo988wQ7vjlLlRuDNtlZVBYGD4rQRaRuDWbHLv7IekIREREtshQd18C4O5LzGxIUweb2b5AN+CjhN1Tzew64Fngandfn+S8Lf4WsLh4Xyor6+6rrITvfncdI0a83OrrtVWmfHugOBRHczIllo4Sh7n7ll/ErBS40t1fa+Hxy4CyNlQ1CFjehvOygdqWnXK5bZDb7Wtr2/LdfXCqg2mJpr7JA/7g7v0Tjl3l7g3GHUdlwwk9y+e4+8sJ+z4lJMzFwEfufmNT8UyYMMFfe61Ft/06OnVy3BsuAmIG1dWtvlybZcq3B4pDcTQnU2LJ9jjMbI67Nzu72haNOTazE4A7CV/LPWFmc939sObOa+t/LGb2WksalY3UtuyUy22D3G5fNratqW/yzOwzMxse9RoPB5Y2clxf4Ang2prEOLr2kujjejP7PXBlCkOvY8iQ9Xz2WY8G+/Py2qtGEZGW29LZKh5z95Hu3t3dh7YkMRYRkXYxAzgn+nwO0OCZEDPrBjwG3Ofuj9QrGx69G3A8YarOdnHBBR/Tq1fdfb16hYfyRETilhUr5ImISLNuBaaY2YfAlGgbM5tgZndHx5wCHAScm2TKthIzext4mzDk5Kb2CvSQQ5ZSXAz5+WBUk995IcXFrofxRCQjpG0qtxQpjjuAdqS2Zadcbhvkdvtyqm3uvgL4epL9rwEXRJ/vB+5v5PzJ7RpgPQUF0cwUvymGiy6C8e8BO6UzBBGRpLIqOY6mg8tJalt2yuW2QW63L5fbllWOPhoWLQrLSYuIZICsSo5FRCTHjBwJP/5x3FGIiGymMcciIhKvDRtg5kxYuTLuSEREsiM5NrPDzewDM5sXLYuaM8zsHjNbambt9mR4XMxslJnNNrP3zOwdM/tO3DGlipn1MLN/mdmbUdtuiDumVDOzzmb2hpn9Ne5YUsnM5pvZ29HDaK2fpFdS75134Kij4M9/jjsSEZHMT47NrDNwF3AEsAtwupntEm9UKXUvcHjcQbSTKuC77r4zsD9wSQ797NYDk919T2AccLiZ7R9zTKn2HeC9uINoJ5PcfVy2zXOcs8aNg223hUceaf5YEZF2lvHJMbAvMM/dP3b3DcB04LiYY0oZd38eyMnvEt19ibu/Hn3+gpBojYg3qtTwoCLa7Bq9tny5yQxhZiOBo4C7mztWZIuZwcknw7PPwooVcUcjIh1cNiTHI4AFCdsLyZEEqyMxs9HAXsAr8UaSOtGwg7mElciedvecaRvwc+AqII2L+aaNA383szlmVhh3MBI5+WTYtAkefzzuSESkg8uG5NiS7MuZHrqOwMz6AH8CLnf3z+OOJ1XcfZO7jwNGAvua2W5xx5QKZnY0sNTd58QdSzs50N33JgzVusTMDoo7IAH23hvGjIHZs+OOREQ6uGyYym0hMCpheySwOKZYpJXMrCshMS5x95x82sbdV5tZKWHseC48WHkgcKyZHQn0APqa2f3ufmbMcaWEuy+O3pea2WOEoVvPxxuVYBYS41Gjmj9WRKQdZUPP8avAWDMbY2bdgNOAGTHHJC1gZgb8DnjP3X8WdzypZGaDzax/9LkncAjwfrxRpYa7X+PuI919NOHf26xcSYzNrLeZbVXzGTiU3PiFJjfk50OnbPhvSURyWcbfhdy9CrgUeIrwQNfD7v5OvFGljpk9CLwE7GhmC83s/LhjSqEDgbOAydG0WXOj3shcMByYbWZvEX6Be9rdc2rKsxw1FHjBzN4E/gU84e5PxhyTJLrrLjj4YHCNnhOReGTDsArcfSYwM+442oO7nx53DO3F3V8g+ZjxrOfubxEeMMxp7l4KlMYcRsq4+8fAnnHHIU3o1g2efx5efRX23TfuaESkA8r4nmMREelATjkFevSAe++NOxIR6aCUHIuISObo1w9OOglKSmDt2rijEZEOSMmxiIhklgsvhM8/hwcfjDsSEemAlByLiEhmOfBA+P73Yfz4uCMRkQ4oKx7IExGRDsQMbr017ihEpINSz7GIiGSmt97Sg3kiknZKjkVEJDNNmxbGHy9bFnckItKBKDkWEZHMdNllsH49/PrXcUciIh2IkmMREclMO+0ExxwDv/oVfPll3NGISAeh5FhERDLXlVfC8uVw331xRyIiHYSSYxERyVxf+xpMmgSrV8cdiYh0EJrKTUREMpcZPPtseBcRSQP1HIuISGYzA3d48cXwLiLSjpQcS4uY2fVmdn8T5ReZ2WdmVmFmW6cztrYys3vNbIOZzW/h8TtE7dtkZhe0c3girWJmA83saTP7MHof0Mhxm8xsbvSakbB/jJm9Ep3/kJl1S1/0LfDYY2HlvKeeijsSEclxSo47gOYS2xRcvyvwM+BQd+/j7ivaq6528FN3H12zYWbdzeweM/vczD41s/+uKXP3/7h7H+AfqQ7CzE4xsxfNrNLMSltw/BlmVmZma83scTMbmFA20Mwei8rKzOyMlp4rWe1q4Fl3Hws8G20n86W7j4texybs/wlwR3T+KuD89g23lY4+GvLy4IYb1HssIu1KybFgwZb8XRgK9ADeiaHuVLseGAvkA5OAq8zs8DTUuxL4OdDsmrlmtnTBHc8AACAASURBVCswDTiL8GdfCSROBHsX/H979x5n13zvf/z1yUUiQl3ClEgy7qVUkENRNUhb1K3HLX7jklaaonqaoocYPccpcWmr9OYQ4UQ1dSl1XBpVl2weh1JBQlxyEclkJAyJRMfExOXz++P7HdbM7JnZs2ff5/18PNZj1vp+11rfz3etPXt/93d/11qsi3m1wH/HbTLZVsrX0cDNcf5m4JhMNzQzAw4G7sxm+4JYbz2YPBmeegoefrjY0YhIBTPXN/CSYmYjgF8BBxC+vNzq7mfHBuSFwHeB9YG/Aj9w9zVmVg28DowHLgGGEHqApsSG3b2AAS3Aa+6+e+ydfAKoAfYEdiM0lK4DvkJorF3p7jfEuC4Gtnf3k9vFuyPwfCzzfeAf7n6wme0X67EjsAD4obs/GbdJV/Yq4CrgG7F+j7n7MXH9I4BLgWrgZeAMd38hg2NZA/zB3bdOpC0BJrj7w2Y2HWhw94sS+W8A33b3v8XlS4Ad3H1cYp1U3O+07mLoqThc42R3r+lincuAanf/f3F5O+AVYDPgE0Kv367uviDm3wK84e4XdLWtu/8z1/WRwjGz1e6+cWL5XXfvMLTCzD4C5gAfAVe4+/+a2TDgKXffPq4zAnjA3XdNs/1EYCJAVVXVXrfddluPY21qamLo0KE93s7WrWOfk0+mpaqK53/9615fpJdtHLmmOBRHd0ollnKP46CDDnrW3cd0u6K7ayqRCegPzAWuBjYg9MZ+JeZ9B1gEbAsMBf4M3BLzqgEHbiA0LHcnNIR3jvkXExpzybJSQD3wRcJdSwYCjxF6EQcDo4G3gUM620diX63lD4jLmxIaaKfEfZ8Ulzfrouy/ALcDm8TlA+O6ewKNwD7x+JwGLAEGZXA8awiN32TaEmBsnJ8OXJrI2yTWoyqRdhzwYppjN6GTMi8AVnc2ZRDzBCDVzTr3AOe3S2sC9gL2IPxsnsw7D7ivu22L/frX1P0EPAzMSzMd3f71BbzbyT62in+3jf8P2wGbA4sS64xo/7pPN+21116ejVmzZmW1nbu7/+537lVV7g0N2e8jF3HkkOJoS3F0VCqxlHscwGzP4L22lH7OFtgb2Ar4sbu/7+4fuPv/xbxa4Jfuvtjdm4DJwDgzS96O77/cfa27zyU0snfvprzp7v6Su38EfJ7QY3x+LHcOMI3QwO2pbwIL3f0Wd//I3W8FXgWO7KTsYcBhhB7hd939Q3d/LK73XeB6d3/a3T9295sJDf8vZxFXd1q/hq5JpK0BNsx0B+5+hbtv3NmUwzjXtEtrjbOrvO62lRLn7mPdfdc00z3AW2a2JUD829jJPpbHv4sJX/T2AN4BNk68n2wNLM9zdbIzYQK8/joMH17sSESkQqlxXFpGAEtjg7G9rYClieWlhF7XqkTam4n5Zj5r7HVmWbv9r/K2P60vBbL5BGofa7p9JcseEct+N82+RgHnmtnq1imuv1UWcXWnKf7dKJG2EVBqww2aaBsjfBZnV3ndbSvl7V7CLyvEv/e0X8HMNjGzQXF+GLA/8HLsUZlF+KWk0+1Lwnrrwfrrw4cfwmuvFTsaEalAahyXlmXAyHa9wa2WExqKrUYSxgy+lcF+OxtYnkxfDmxqZskexJHAGxnsv732sabbV7LsZbHsdD2ry4Ap7Xpgh8Te6O68TxgLDYCZ9Sf8fJxWbJyvoG2P++704EJDM7sw3u4t7ZTpfrrxUjJGM9sWGEQY270AGGBmO3RSh662lfJ2BfA1M1sIfC0uY2ZjzKx1fPzOwGwzm0toDF/h7i/HvPOBc8xsEWH8+o0Fjb6njj8eDj8cPkrXlyAikj01jkvLPwiNsyvMbAMzG2xm+8e8W4EfxXuRDgUuA27vpJe5vbeA6q7uCuHuy4AngctjuV8i3MppRhb1mAnsGG8ZNsDMTgR2Ae7vpOwVwAPAtbFna6CZfTVm3wCcYWb7xDtbbGBm32zXiO/MAmBwXH8gcBGhIdiV3wMXxTi+QBjWMT2DslrrcpmH29mlnTrbzsz6m9lgwq8B/eI5GNjJ6jOAI83sADPbAPgp8Gd3/6e7v08Yj/7TeKz2J4xHvaW7bTOto5Qmd1/p7oe4+w7x76qYPtvdJ8T5J919N3ffPf69MbH9Ynff2923d/fj3b2lWHXJyHe+AwsWwE03FTsSEakwahyXEHf/mDAud3vCBWsNwIkx+yZCA+dxwp0pPgB+kOGu/xT/rjSz57pY7yTCxXXLgbuB/3T3h3pQBSB8SANHAOcCK4F/B45w93e62OwU4EPC2ORGYFLc12xCA/W3hIv6FhHuypFJHGuAswhjp98g9CQ3dLPZfwKvEYaBPAb83N3/mkl5vXQKsBb4b8KdStYSvhgAEHueDwBw95eAMwgN3UbCeOGzEvs6i3BhZiPhS9WZcZtMthUpD0ceGR4KcvHF0Nxc7GhEpIKk+/leisjd60lzf1F3/4TQy/fTNHlLCLdqS6bVJOZXEi62S5ufSGsgNGrTxXVxFzGnK///CHdPSLd+urJX8dl4yfZ5fyXcuq7H3H06bXt+f5GY/xCYZGYnuft2cf0Wwp1BvtN+X3GowjPAevSgNznLONvnD223/Efgj52su4ou7lHb1bYiZcMMrrgCDjgArroKfvKTYkckIhVCPcfSZ7n7d+Nwh+0yXH9hYszz9DyHJyLd+cpX4Nhj4W9/01PzRCRn1HMsIiLl68YbYejQXj8QRESklXqORUSkfH3uc9C/P6xaBQsXFjsaEakAOek5NrObCGNVGz3N40bbGzZsmFdXV2e8/1Wr4I03YN26cIvL4cNh002zj7dUykp6//332WCDDfJfUBGobuWrkuuXbd2effbZd9y901sCShG4Q01NuP/x3/8O/dTvIyLZy9WwiumEuwn8PpOVq6urmT17dkY7njEDJk4MjVUIf996Cy65BGprswu2FMpqL5VKUVNTk99CikR1K1+VXL9s62Zm7R9wI8VmBj/+MZx6KtxyC5yW9tpeEZGM5KRx7O6Pm1l1LvbVXl1dx7v0NDdD3elvUnvDODjhBDjrrJB4+OEddzB+fJjeeQeOO65j/plnwoknwrJl1J0+kOaWz3csqw5qx8yH732v4/YXXQRjx8KcOTBpUsf8yy6D/faDJ5+ECy/smH/NNTB6dKf1FxGRDNTWwrXXhkbyUUfBJpsUOyIRKVMFuyDPzCYCEwGqqqpIpVIZbVdffyDt7hIW0lu2YPXq1TQuWMDyVIp+H3zAl1av7rDem6++ypupFAPXrOGLafLfeOkl3k6lGNTYSH1LmsYzUF/vPP300+yUZvulc+fy7oABDF20iO3T5C9+7jneW7eOjebNY9s0+Ytmz2bgI48weO1aUmlLL39NTU0Zn+9yU8l1g8quXyXXrU/q1w+uuw722gsmTw7zIiJZKFjj2N2nAlMBxowZ45n+nDlyJCxN8yPmyFH92HjOHDYGdmxNPPTQDuttDHyhdeHoo9Pmf7rPf++krJHGPqeeGn6y62z7mhqYMKFD/p7J/LPP7pA/JuatXr2ajS+6qGPhFUA/zZevSq5fJdetz9p9d/i3fwtv5B9/HC7UExHpoZK/amHKFBgypG3akCEhvZzLEhGRPPj5z+Guu9QwFpGslXzjuLYWpk6FUaPAzBk1Kizn4wK5tmWR17JERCQPWhvFCxbAn/9c3FhEpCzlpHFsZrcCfwd2MrMGMzs9F/ttVVsLS5bAo48+xpIl+W2stpb1ySfkvSwREcmTyZPDULglS4odiYiUmZw0jt39JHff0t0HuvvW7n5jLvYrIiKSlauvDj8BTpyoR0uLSI+U/LCKPuH665l/zjnFjkJEpHKMHBnGHz/0ENx0U7GjEZEyosZxKdhpJ9aOHFnsKEREKsvEieFOQeecAw0NxY5GRMqEGsel4L772OzJJ4sdhYhIZenXD6ZNC7fZ1ENBRCRDahyXgquuYsQddxQ7ChGRyrPddnDVVbDBBhp7LCIZUeNYREQq35w5sM8+UF9f7EhEpMSpcSwiIpVvo43glVdg/Phwr04RkU6ocSwiIpVv223hV7+CWbPCbd5ERDqhxrGIiPQN3/42HHMMXHghvPBCsaMRkRKlxnEpuOUWXrnwwmJHISJS2cxg6tRw54rf/KbY0YhIiVLjuMhmzIDqA0aw/7jjqa4OyyIikiebbw6PPw7XXVfsSESkRKlxXEQzZoR71C9dCu7G0qVhWQ1kEZE82nFH6N+fgatWwRNPFDsaESkxA4odQF9WVwfNzW3Tmpuh7vQ3qf3GABg2DKZPD1N7M2fCkCFw7bWQ7h7JqVT4+4tfwP33t81bf3144IEc1EBESoWZbQrcDlQDS4AT3P3dduscBCSvRvsCMM7d/9fMpgMHAmti3nh3n5PnsIvqCz/7GSxcCHPnwtZbFzscESkR6jkuos5ut1nfskVhAxGRSnAB8Ii77wA8EpfbcPdZ7j7a3UcDBwPNwN8Sq/y4Nb/SG8YAi77/fWhpYcYhN1I9yunXDw1vExH1HBfTyJFhSEWH9FH9Qq8xhHtyjh/f+U7OOitMnTnvvDCJSKU7GqiJ8zcDKeD8LtY/DnjA3Zu7WKeirR0xghmn/JWJ1+1BMwbw6fA2gNraIgYnIkWjxnERTZkS3oSTQyuGDAnpeXXJJeHvT36S54JEpICq3H0FgLuvMLPufoIaB/yyXdoUM/sPYs+zu7e038jMJgITAaqqqki1DuHqgaampqy2y7WmpibOvXsszQxuk97cDOee+wHDhz9VsDhK5XgojtKLA0onlr4ShxrHRdTaK1FXB/X1zsiRxpQpBeiteOSR8FeNY5GyYmYPA59Pk1XXw/1sCewGPJhIngy8CawHTCX0Ov+0/bbuPjXmM2bMGK+pqelJ0QCkUimy2S7XUqkUjY2D0+Y1Ng4uWIyldDwUR+nFAaUTS1+JQ43jIqutDVMq9VhJvOBEpHS5+9jO8szsLTPbMvYabwk0drGrE4C73f3DxL5XxNkWM/sfoE+Mx+p0eNvIwsciIqVBF+SJiFSGe4HT4vxpwD1drHsScGsyITaoMTMDjgHm5SHGkjNlShjOllSQ4W0iUrLUOBYRqQxXAF8zs4XA1+IyZjbGzKa1rmRm1cAI4LF2288wsxeBF4FhwKUFiLnoamvDQ/NGjQoP0Bs1KizrYjyRvkvDKvqizTYrdgQikmPuvhI4JE36bGBCYnkJMDzNegfnM75S1jq8TUQE1Djum+66q9gRiIiIiJQkDasQEREREYnUOO6LJk8Ok4iIiIi0kZPGsZkdambzzWyRmXV4ZKmUjhkzoPrqH9Lviil5f0zqjBnhUawHH3xgQR7J2lpeJT4CttB1K+S5q+S6iYhI+en1mGMz6w/8jnB1dAPwjJnd6+4v93bfklszZsQn8rWEZwjk8zGpn5bVDGB5fyRr2/Iq6xGwha5bIc9dJddNRETKUy4uyNsbWOTuiwHM7DbgaECN4xJTV9f2UdUQluvqoPaZSTBnTtvMHXcM9zSC0IJYsKBt/ujRcM01Yf7kk6Gh4bOynrrt00Z4m7JOf5PaG8aFhEMO+ewpfYcdBmvXtt3/EUfAefE5BOkekHLCCXDWWdDcTN3p76Uvrw5qv/EOHHdcx+3PPBNOPBGWLYNTTumYf+65cOSRMH8+fO97HfMvuggG5P+a1k7PW/JYdnEuANh3X7j88jB/7LGwcmXb/MS5qJvwFs0fVHUsry42ILs5Fxx+eMf88ePD9E7bc5HR6wQyOxdjx4bX8KRJHfMvuwz224+6cz+gubnjo4I/rZuIiPR5ufhkHw4sSyw3APu0X8nMJgITAaqqqrJ6JnapPNM7HwpRt/r6AwFLk+40NDQwdPXqNunNy5ezIMa04/LlDGmX39TQwKKYv/NbbzEokV/fskX6GFq2YHVc793XX2dp3H63Vavo39LSZt2Vr73Gspg/ul3ZAI0LFrA8laLfBx9Q3/L1TursPPHEE3wxzfZvvPQSb6dSDGpsZOc0+ctefJGVG27I+vX17JQmf+ncuTTttFPxzlviWHZ1LgDW1Nfzesz/4ttvM/C999rkJ89F/Qdf7SQOJ5V6rNtz8aU0+W+++ipvplIMXLOmzbnI5HUCmZ2LdwcMYOiiRWyfJn/xc8/x3rp11L91YJd1ExERwd17NQHHA9MSy6cAv+lqm7322suzMWvWrKy2KweFqNuoUe7QcRo1qrzLKkZ57u7+/PP+zA035LGAoJKPZTnWDZjtvXzfrJSp3N/LFUdbiqOtUonDvXRiKfc4Mn3/zsUFeQ2Epy212hpYnoP9So4V8jGphX4ka1EeATtpEtv/9rd5LCCo5GNZyXUTEZHylIvG8TPADma2jZmtB4wD7s3BfiXHCvmY1LZled4fyVrJj4D9tG6D3sT4pMDHMr/nrtDnrdCvSxERKT+9HnPs7h+Z2dnAg0B/4CZ3f6nXkUleFPIxqa1lpVKPUZPuIq48lVeJamv57AK1Aoy7L+S5K/R5K/TrUkREyktOLrV395nAzFzsS0RERESkWPJ/HyoRyY3Ro4sdgYiISMVT41gkW5ddxuLnnmPPQpXXeh9jERERyRs1jkWytd9+vLduXbGjEBERkRzKxd0qRPqmJ59ko3nzClfeySeHSURERPJGPcci2brwQrZdvRrOPrsw5bV/JLSIiIjknHqORUREREQiNY5FRERERCI1jkVEREREIo05FikX++5b7AhEREQqnhrHItm65hoWzZ7NmEKVd/nlhSpJRESkz1LjWCRbo0fTtHp1saMQERGRHNKYY5FsPfwwmzz7bOHKO/bYMImIiEjeqHEskq1LL2XULbcUrryVK8MkIiIieaPGsYhIBTCz483sJTP7xMw6HQpvZoea2XwzW2RmFyTStzGzp81soZndbmbrFSZyEZHSosaxiEhlmAf8K/B4ZyuYWX/gd8BhwC7ASWa2S8y+Erja3XcA3gVOz2+4IiKlSY1jEZEK4O6vuPv8blbbG1jk7ovdfR1wG3C0mRlwMHBnXO9m4Jj8RSsiUrp0twqRcnHIIcWOQMrfcGBZYrkB2AfYDFjt7h8l0oen24GZTQQmAlRVVZFKpXocRFNTU1bb5ZriUBzlEAeUTix9JQ41jkWydf31zH/6afYpVHk/+UmhSpISZWYPA59Pk1Xn7vdksos0ad5FesdE96nAVIAxY8Z4TU1NBsW2lUqlyGa7XFMciqMc4oDSiaWvxKHGsUi2dtqJtStWFDsK6UPcfWwvd9EAjEgsbw0sB94BNjazAbH3uDVdRKTP0ZhjkWzddx+bPflk4co77LAwiWTvGWCHeGeK9YBxwL3u7sAs4Li43mlAJj3RIiIVR41jkWxddRUj7rijcOWtXRsmkTTM7Ftm1gDsC/zFzB6M6VuZ2UyA2Ct8NvAg8Apwh7u/FHdxPnCOmS0ijEG+sdB1EBEpBRpWIZKFGTOg7qnbqG/ZgpHVMGUK1NYWOyrpy9z9buDuNOnLgcMTyzOBmWnWW0y4m4WISJ+mxrFID82YARMnQnNLuC5q6dKwDGogi4iIlLteNY7N7HjgYmBnYG93n52LoERKWV0dNDe3TWtuhrpJ71N7wzc7bnDnnTBsGEyfHqb2Zs6EIUPg2msh3TCN1tvVzJsHu+7ay+hFRESkK73tOW59ItP1OYhFpCzU13eSvnJIfgu+4ALYaKP8liEiItLH9apx7O6vAISHK4n0DSNHhqEUHdPts17edMaPD1NnzjorTJ0577wMIxQREZFs6W4VIj00ZUoYBZE0ZEhIFxERkfLWbc9xDp7I1LqfinnkaD6obuVj+HD40Y+2YNq0bWlsHMQWW7QwYcJihg9v7LLjuBxV2rlLquS6iYhI9rptHOfgiUyt+6mYR47mg+pWXmpq4NJLk3XbJU6VpRLPXatKrpuIiGRPwypERERERCILTw3NcmOzbwG/ATYHVgNz3P0bGWz3NpDmkqZuDQPeyWK7cqC6ladKrhtUdv2yrdsod98818GUowp4L1ccbSmOtkolDiidWMo9jozev3vVOC40M5vt7mOKHUc+qG7lqZLrBpVdv0quW6krlWOvOBRHOcQBpRNLX4lDwypERERERCI1jkVEREREonJrHE8tdgB5pLqVp0quG1R2/Sq5bqWuVI694mhLcbRVKnFA6cTSJ+IoqzHHIiIiIiL5VG49xyIiIiIieaPGsYiIiIhIVBaNYzM71Mzmm9kiM7ug2PHkkpndZGaNZjav2LHkmpmNMLNZZvaKmb1kZj8sdky5YmaDzewfZjY31u2/ih1TrplZfzN73szuL3YsuWRmS8zsRTObY2azix1PpTKz4+P/xidm1uktlzp7fzezbczsaTNbaGa3m9l6WcaxqZk9FPfzkJltkmadg+LroXX6wMyOiXnTzez1RN7ofMUR1/s4Uda9ifRCHo/RZvb3eP5eMLMTE3m9Oh7dfZ6b2aBYv0WxvtWJvMkxfb6ZdftMhV7GcY6ZvRzr/4iZjUrkpT1HeYpjvJm9nShvQiLvtHgeF5rZaXmO4+pEDAvMbHUiL5fHo8s2kQW/jnG+YGZ7JvJydjxw95KegP7Aa8C2wHrAXGCXYseVw/p9FdgTmFfsWPJQty2BPeP8hsCCSjl3gAFD4/xA4Gngy8WOK8d1PAf4I3B/sWPJcb2WAMOKHUelT8DOwE5AChjTyTqdvr8DdwDj4vx1wJlZxvEz4II4fwFwZTfrbwqsAobE5enAcTk4HhnFATR1kl6w4wHsCOwQ57cCVgAb9/Z4ZPJ5DpwFXBfnxwG3x/ld4vqDgG3ifvrnMY6DEq+BM1vj6Ooc5SmO8cBvO3mdLo5/N4nzm+Qrjnbr/wC4KdfHI+6ryzYRcDjwAOEz+MvA07k+Hu5eFj3HewOL3H2xu68DbgOOLnJMOePujxPeiCuOu69w9+fi/D+BV4DhxY0qNzxoiosD41QxV7ea2dbAN4FpxY5FypO7v+Lu87tZLe37u5kZcDBwZ1zvZuCYLEM5Om6f6X6OAx5w9+Ysy8tVHJ8q9PFw9wXuvjDOLwcaCU/C7a1MPs+T8d0JHBLrfzRwm7u3uPvrwKK4v7zE4e6zEq+Bp4CtsyyrV3F04RvAQ+6+yt3fBR4CDi1QHCcBt2ZZVpcyaBMdDfw+fgY/BWxsZluS2+NRFo3j4cCyxHIDFdLA6kviT2N7EHpYK4KFYQdzCB8cD7l7xdQNuAb4d+CTYgeSBw78zcyeNbOJxQ6mj+vs/X0zYLW7f9QuPRtV7r4Cwhd2YItu1h9Hxw/+KfEn3KvNbFCe4xhsZrPN7KnWoR0U8XiY2d6E3sTXEsnZHo9MPs8/XSfWdw2h/rlsC/R0X6cTeitbpTtH+Yzj2Hi87zSzET3cNpdxEIeXbAM8mkjO1fHIRGex5rStOCDbDQvI0qRVTA9dX2BmQ4G7gEnu/l6x48kVd/8YGG1mGwN3m9mu7l72Y8fN7Aig0d2fNbOaYseTB/u7+3Iz2wJ4yMxejb0V0kNm9jDw+TRZde5+Tya7SJPmXaT3OI4MYkjuZ0tgN+DBRPJk4E1CA3EqcD7w0zzGMTK+PrcFHjWzF4F075uFOh63AKe5e+sX5YyPR7pdpklrX4+cvCZyEEdY0exkYAxwYCK5wzly99fSbZ+DOO4DbnX3FjM7g9CrfnCG2+YyjlbjgDvj51+rXB2PTBTi9VEWjeMGYERieWtgeZFikR4ys4GEhvEMd/9zsePJB3dfbWYpwk84Zd84BvYHjjKzw4HBwEZm9gd3P7nIceVE/JkYd280s7sJPymqcZwFdx/by1109v7+DuHn0gGx97DL9/2u4jCzt8xsS3dfERt7jV3EcwJwt7t/mNj3ijjbYmb/A5yXzzgSr8/F8X1lD8J7aEGPh5ltBPwFuCj+fN2674yPRxqZfJ63rtNgZgOAzxF+Zs9lWyCjfZnZWMIXigPdvaU1vZNzlE1jsNs43H1lYvEG4MrEtjXttk1lEUNGcSSMA77fLsZcHY9MdBZrLo9HWQyreAbYwcKVuusRTkyvroaUwojjxG4EXnH3XxY7nlwys81jjzFmtj4wFni1uFHlhrtPdvet3b2a8P/2aKU0jM1sAzPbsHUe+DqV8YWmXKV9f/dwhc0swvhfgNOATHqi07k3bp/JfjqMpYwNyNb3s2PI/vXSbRxmtknrMAUzG0b4ovpyoY9HPBd3E8Z2/qldXm+ORyaf58n4jiO8/3hMH2fhbhbbADsA/+hB2T2Kw8z2AK4HjnL3xkR62nOUxzi2TCweRbh2B8KvG1+P8WxCeC9L/uKR0zhiLDsRLnb7eyItl8cjE/cCp1rwZWBN/MKWy+NR+ner8M+uTlxA+CZSV+x4cly3WwlXAn9I+OZzerFjymHdvkL4WeMFYE6cDi92XDmq25eA52Pd5gH/UeyY8lTPGirobhWEq7HnxumlSns/KaUJ+FZ8T2sB3gIejOlbATMT66V9f4/n6h+EC6/+BAzKMo7NgEeAhfHvpjF9DDAtsV418AbQr932jwIvxv/zPxDvUpOPOID9Yllz49/TE9sX7HgAJ8fPpDmJaXQujke6800YlnFUnB8c67co1nfbxLZ1cbv5wGG9fH12F8fD8XXbWv97uztHeYrjcsJ71VzCF6QvJLb9TjxOi4Bv5zOOuHwxcEW77XJ9PDq0iYAzgDNivgG/i3G+SOJOOLk8Hnp8tIiIiIhIVA7DKkRERERECkKNYxERERGRSI1jEREREZFIjWMRERERkUiNYxERERGRSI1jERERKTozO8PMTo3z481sq0TeNDPbpXjRSV+iW7mJiIhISYlPWjvP3WcXOxbpe9RzLCIiIr1iZtVm9qqZ3WxmL5jZnWY2xMwOMbPnzexFM7sp8TS1K8zs5bjuL2LaxWZ2npkdR3goyQwzm2Nm65tZyszGxPVOivubZ2ZXJmJoMrMpZjbXzJ4ys6piHAspf2oci4iISC7sBEx19y8B7wHnANOBE919N2AAcKaZbUp4g0Z3NAAAAW1JREFUguIX47qXJnfi7ncCs4Fadx/t7mtb8+JQiyuBg4HRwL+Y2TExewPgKXffHXgc+G7eaioVTY1jERERyYVl7v5EnP8DcAjwursviGk3A18lNJw/AKaZ2b8CzT0o41+AlLu/7e4fATPiPgHWAffH+WcJjwQX6TE1jkVERCQXMrqIKTZq9wbuAo4B/tqDMqyLvA/9swupPib0VIv0mBrHIiIikgsjzWzfOH8S8DBQbWbbx7RTgMfMbCjwOXefCUwiDI9o75/AhmnSnwYONLNhZtY/lvNYLishom9VIiIikguvAKeZ2fXAQuCHwFPAn8xsAPAMcB2wKXCPmQ0m9AT/KM2+pgPXmdlaoLXBjbuvMLPJwKy47Ux3vyd/VZK+SLdyExERkV4xs2rgfnfftcihiPSahlWIiIiIiETqORYRERERidRzLCIiIiISqXEsIiIiIhKpcSwiIiIiEqlxLCIiIiISqXEsIiIiIhL9f7gA+88e2RI9AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#@title Interactive { run: \"auto\" }\n", "\n", "N = 10 #@param {type: \"slider\", min:1, max:20, step:1}\n", "h = 0.5 #@param {type:\"slider\", min:0, max:1, step:0.01}\n", "gamma = 0.54 #@param {type:\"slider\", min:0, max:1, step:0.01}\n", "x_initial = -0.72 #@param {type:\"slider\", min:-1, max:1, step:0.01}\n", "v_initial = -0.76 #@param {type:\"slider\", min:-1, max:1, step:0.01}\n", "\n", "model = mpc_double_integrator(N, h)\n", "model.gamma = gamma\n", "model.ic[1] = x_initial\n", "model.ic[2] = v_initial\n", "\n", "SolverFactory('cbc').solve(model)\n", "plot_results(model)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "n8wM8nuC8qVO" }, "source": [ "## Model predictive control as a feedback controller\n", "\n", "Model Predictive Control is a control strategy that uses open-loop optimal control calculations to implement feedback control. The concept behind MPC is to continually update an optimal control policy as new sensor information becomes available. Then at each point in time, the manipulated variable is set to the first value in the updated control policy. \n", "\n", "For low dimensional systems like the double integrator, it is possible to compute optimal control policies for all feasible initial conditions. The control input is then the first value of the resulting control policy. The result can be written as a function\n", "\n", "$$u(\\tau) = mpc(x_1(\\tau), x_2(\\tau))$$\n", "\n", "The following cell demonstrates the calculation of the control policy as a function initial conditions. The result will be a matrix $U$ of control values computed for 2D grid of values for initial position and velocity." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 466 }, "colab_type": "code", "executionInfo": { "elapsed": 308477, "status": "ok", "timestamp": 1555797382017, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg", "userId": "09038942003589296665" }, "user_tz": 240 }, "id": "-KqWLg1sqcie", "outputId": "1b7d2448-6e87-451b-b8b5-e4445209aa52" }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'control force')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# turn off pyomo warnings\n", "logging.getLogger('pyomo.core').setLevel(logging.ERROR)\n", "\n", "model = mpc_double_integrator(10)\n", "model.h = 0.5\n", "model.gamma = 0.4\n", "\n", "def fun(y, v):\n", " u = 0*y\n", " for i in range(0, len(y)):\n", " model.ic[1] = y[i]\n", " model.ic[2] = v[i]\n", " results = SolverFactory('cbc').solve(model)\n", " if str(results.solver.termination_condition) == 'optimal':\n", " u[i] = model.u[0]()\n", " else:\n", " u[i] = None\n", " return u\n", "\n", "fig = plt.figure(figsize=(10,8))\n", "ax = fig.add_subplot(111, projection='3d')\n", "\n", "y = v = np.arange(-0.7, 0.7, 0.1)\n", "Y, V = np.meshgrid(y, v)\n", "u = np.array(fun(np.ravel(Y), np.ravel(V)))\n", "U = u.reshape(V.shape)\n", "\n", "ax.plot_surface(V, Y, U)\n", "ax.set_xlabel('initial velocity')\n", "ax.set_ylabel('initial position')\n", "ax.set_zlabel('control force')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results of the MPC calculation are recorded in a matrix $U$. In the next cell we create 2D interpolation object that will be used for simulation of the closed-loop system." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "mpc = interp2d(Y, V, U)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we perform a continuous time simulation where the interpolator is used for feedback control. Compare this result to one obtained above for same initial condition." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "colab": {}, "colab_type": "code", "id": "vby0kX9NRAqO" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def mpc_sim(x, t):\n", " y, v = x\n", " return [v, mpc(y,v)]\n", "\n", "t = np.linspace(0, 10, 200)\n", "x = odeint(mpc_sim, [-0.75, -0.75], t)\n", "\n", "plt.subplot(2,1,1)\n", "plt.plot(t,x)\n", "plt.xlabel('time')\n", "plt.legend(['Position', 'Velocity'])\n", "plt.grid(True)\n", "\n", "plt.subplot(2,1,2)\n", "plt.plot(t, [mpc(x1, x2) for x1,x2 in x])\n", "plt.xlabel('time')\n", "plt.legend(['Control input u'])\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "Copy of 02.05-Model-Predictive-Control-of-a-Double-Integrator.ipynb", "provenance": [ { "file_id": "1wdOLC3Y2I2rUlh4ZSkwVmOJwO8NHN-gs", "timestamp": 1556022553088 } ], "version": "0.3.2" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 4 }