test4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using LinearAlgebra\n",
    "using Plots\n",
    "using StaticArrays\n",
    "using TrajectoryOptimization\n",
    "import TrajectoryOptimization:dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dynamics (generic function with 9 methods)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "struct Qubit <: AbstractModel\n",
    "      n::Int\n",
    "      m::Int\n",
    "end\n",
    "\n",
    "function dynamics(model::Qubit,x,ü)\n",
    "      #Pauli spin matrices\n",
    "      i2 = SMatrix{2,2}([0 -1; 1 0]) #2x2 unit imaginary matrix\n",
    "      # Sx = SMatrix{4,4}([zeros(2,2) I; I zeros(2,2)])\n",
    "      # Sy = SMatrix{4,4}([zeros(2,2) -i2; i2 zeros(2,2)])\n",
    "      # Sz = SMatrix{4,4}([I zeros(2,2); zeros(2,2) -I])\n",
    "      iSx = SMatrix{4,4}([zeros(2,2) i2; i2 zeros(2,2)])\n",
    "      # iSy = SMatrix{4,4}([zeros(2,2) I; -I zeros(2,2)])\n",
    "      iSz = SMatrix{4,4}([i2 zeros(2,2); zeros(2,2) -i2])\n",
    "\n",
    "      u̇ = x[9]\n",
    "      u = x[10]\n",
    "      ẋ = [(-iSx - u.*iSz)*x[1:4]; (-iSx - u.*iSz)*x[5:8]; ü; u̇; u]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Qubit(11, 1)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2*4 + 3 # state dimension\n",
    "m = 1     # input dimension\n",
    "model = Qubit(n,m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 0.01 #time step\n",
    "N = 101 #number of knot points\n",
    "tf = dt*(N-1)\n",
    "\n",
    "#initial state(s)  \n",
    "x0 = @SVector [1.0, 0, 0, 0,       # |0> \n",
    "               0, 0, 1.0, 0,     # |1>\n",
    "               0, 0, 0]          # controls\n",
    "#final state(s) for Y pi/2 gate\n",
    "xf = @SVector [1/sqrt(2), 0, 1/sqrt(2), 0,\n",
    "              -1/sqrt(2), 0, 1/sqrt(2), 0,\n",
    "               0, 0, 0] #desired final state\n",
    "\n",
    "U0 = [@SVector randn(m) for k = 1:N-1] #random initial guess for control inputs\n",
    "X0 = [@SVector fill(NaN,n) for k = 1:N];\n",
    "Z = Traj(X0,U0,dt*ones(N));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Set up quadratic objective function\n",
    "Q = Diagonal(@SVector [1e-3, 1e-3, 1e-3, 1e-3, \n",
    "                       1e-3, 1e-3, 1e-3, 1e-3,\n",
    "                       1, 1, 1e-3])\n",
    "R = 1.0*Diagonal(@SVector ones(m))\n",
    "Qf = 1.0*Diagonal(@SVector ones(n))\n",
    "obj = LQRObjective(Q,R,Qf,xf,N);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Set up constriants\n",
    "goal = GoalConstraint(xf)\n",
    "con_goal = ConstraintVals(goal, N:N)\n",
    "conSet = ConstraintSet(n,m,[con_goal], N);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Set up and solve traj. opt. problem\n",
    "prob = Problem{RK3}(model, obj, conSet, x0, xf, Z, N, tf)\n",
    "opts = ALTROSolverOptions{Float64}(verbose=true,projected_newton=false)\n",
    "solver = ALTROSolver(prob, opts)\n",
    "solve!(solver)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "X̃ = states(solver)\n",
    "X1 = zeros(4,N)\n",
    "X2 = zeros(4,N)\n",
    "U = zeros(N)\n",
    "U̇ = zeros(N)\n",
    "for k = 1:N\n",
    "      X1[:,k] = X̃[k][1:4]\n",
    "      X2[:,k] = X̃[k][5:8]\n",
    "      U[k] = X̃[k][9]\n",
    "      U̇[k] = X̃[k][10]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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   "source": [
    "plot(X1',xlabel=\"time step\",title=\"State Trajectory 1\",label=[\"Re(x1)\" \"Im(x1)\" \"Re(x2)\" \"Im(x2)\"])"
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  {
   "cell_type": "code",
   "execution_count": 19,
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    "plot(X2',xlabel=\"time step\",title=\"State Trajectory 2\",label=[\"Re(x1)\" \"Im(x1)\" \"Re(x2)\" \"Im(x2)\"])"
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  {
   "cell_type": "code",
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