{ "cells": [ { "cell_type": "markdown", "id": "03aa22e7", "metadata": {}, "source": [ "# Stochastic Response\n", "Richard M. Murray, 6 Feb 2022\n", "\n", "This notebook illustrates the implementation of random processes and stochastic response. We focus on a system of the form\n", "\n", "$$\n", " \\dot X = A X + F V \\qquad X \\in {\\mathbb R}^n\n", "$$\n", "\n", "where $V$ is a white noise process and the system is a first order linear system." ] }, { "cell_type": "code", "execution_count": 1, "id": "902af902", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "import control as ct\n", "from math import sqrt, exp\n", "\n", "# Fix random number seed to avoid spurious figure regeneration\n", "np.random.seed(1)" ] }, { "cell_type": "markdown", "id": "d020a2ec", "metadata": {}, "source": [ "We begin by defining a simple first order system\n", "\n", "$$\n", "\\frac{dX}{dt} = - a X + V, \\qquad Y = c X\n", "$$\n", "\n", "and a (scalar) white noise signal $V$ with intensity $Q$." ] }, { "cell_type": "code", "execution_count": 2, "id": "60192a8c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# First order system\n", "a = 1\n", "c = 1\n", "sys = ct.ss([[-a]], [[1]], [[c]], 0)\n", "\n", "# Create the time vector that we want to use\n", "Tf = 5\n", "T = np.linspace(0, Tf, 1000)\n", "dt = T[1] - T[0]\n", "\n", "# Create the basis for a white noise signal\n", "Q = np.array([[0.1]])\n", "V = ct.white_noise(T, Q)\n", "\n", "plt.plot(T, V[0])\n", "plt.xlabel('Time [s]')\n", "plt.ylabel('$V$');" ] }, { "cell_type": "markdown", "id": "b4629e2c", "metadata": {}, "source": [ "Note that the magnitude of the signal seems to be much larger than $Q$. This is because we have a Gaussian process $\\implies$ the signal consists of a sequence of \"impulse-like\" functions that have magnitude that increases with the time step $dt$ as $1/\\sqrt{dt}$ (this gives covariance $\\mathbb{E}(V(t_1) V^T(t_2)) = Q \\delta(t_2 - t_1)$." ] }, { "cell_type": "code", "execution_count": 3, "id": "23319dc6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mean(V) [0.0] = 0.17348786109316244\n", "cov(V) * dt [0.1] = 0.09633133133133133\n" ] } ], "source": [ "# Calculate the sample properties and make sure they match\n", "print(\"mean(V) [0.0] = \", np.mean(V))\n", "print(\"cov(V) * dt [%0.3g] = \" % Q.item(), np.round(np.cov(V), decimals=3) * dt)" ] }, { "cell_type": "markdown", "id": "3196c60d", "metadata": {}, "source": [ "The response of the system to white noise can be computed using the `input_output_response` function:" ] }, { "cell_type": "code", "execution_count": 4, "id": "2bdaaccf", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Response of the first order system\n", "T, Y = ct.input_output_response(sys, T, V)\n", "plt.plot(T, Y)\n", "plt.xlabel('Time [s]')\n", "plt.ylabel('$Y$');" ] }, { "cell_type": "markdown", "id": "ead0232e", "metadata": {}, "source": [ "This is a first order system, and so we can compute the analytical correlation function and compare this to the sampled data:" ] }, { "cell_type": "code", "execution_count": 5, "id": "d31ce324", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* mean(Y) [0] = 0.161\n", "* cov(Y) [0.05] = 0.013\n" ] } ], "source": [ "# Compare static properties to what we expect analytically\n", "def r(tau):\n", " return c**2 * Q / (2 * a) * exp(-a * abs(tau))\n", " \n", "print(\"* mean(Y) [%0.3g] = %0.3g\" % (0, np.mean(Y)))\n", "print(\"* cov(Y) [%0.3g] = %0.3g\" % (r(0).item(), np.cov(Y)))" ] }, { "cell_type": "markdown", "id": "28321bee", "metadata": {}, "source": [ "Finally, we look at the correlation function for the input and the output:" ] }, { "cell_type": "code", "execution_count": 6, "id": "1cf5a4b1", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Correlation function for the input\n", "tau, r_V = ct.correlation(T, V)\n", "\n", "plt.plot(tau, r_V, 'r-')\n", "plt.xlabel(r'$\\tau$')\n", "plt.ylabel(r'$r_V(\\tau)$');" ] }, { "cell_type": "code", "execution_count": 7, "id": "62af90a4", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Correlation function for the output\n", "tau, r_Y = ct.correlation(T, Y)\n", "plt.plot(tau, r_Y)\n", "plt.xlabel(r'$\\tau$')\n", "plt.ylabel(r'$r_Y(\\tau)$')\n", "\n", "# Compare to the analytical answer\n", "plt.plot(tau, [r(t)[0, 0] for t in tau], 'k--');" ] }, { "cell_type": "markdown", "id": "2a2785e9", "metadata": {}, "source": [ "The analytical curve may or may not line up that well with the correlation function based on the sample. Try running the code again with a different random seed to see how things change based on the specific random sequence chosen at the start.\n", "\n", "Note: the _right_ way to compute the correlation function would be to run a lot of different samples of white noise filtered through the system dynamics and compute $R(t_1, t_2)$ across those samples. The `correlation` function computes the covariance between $Y(t + \\tau)$ and $Y(t)$ by varying $t$ over the time range." ] }, { "cell_type": "code", "execution_count": null, "id": "bd5dfc75", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 5 }