{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Optimal Control and Parameter Identification of Dynamcal Systems with Direct Collocation and SymPy\n", "\n", "Jason K. Moore \n", "July 8, 2015 \n", "SciPy 2015, Austin, Texas, USA\n", "\n", "
\n", "\n", " | \n", "\n", "\n", " | \n", "\n", "\n", " | \n", "
\n",
" \n",
" Earth: g=9.8 m/s-2 \n", " | \n",
" \n",
" \n",
" Moon: g=1.6 m/s-2 \n", " | \n",
"
$$\\dot{\\mathbf{x}} = \\mathbf{f}_o(\\mathbf{x}, \\mathbf{r}_c, \\mathbf{r}_k, \\mathbf{p}_k, t)$$
\n", "\n", " | Known | \n", "Identified | \n", "Error | \n", "
---|---|---|---|
$k_{00}$ | \n", "950 | \n", "946 | \n", "-0.4% | \n", "
$k_{01}$ | \n", "175 | \n", "177 | \n", "1.4% | \n", "
$k_{02}$ | \n", "185 | \n", "185 | \n", "-0.2% | \n", "
$k_{03}$ | \n", "50 | \n", "55 | \n", "9.4% | \n", "
$k_{10}$ | \n", "45 | \n", "45 | \n", "1.1% | \n", "
$k_{11}$ | \n", "290 | \n", "289 | \n", "-0.3% | \n", "
$k_{12}$ | \n", "60 | \n", "59 | \n", "-2.1% | \n", "
$k_{13}$ | \n", "26 | \n", "27 | \n", "4.2% | \n", "