test_AFTI16.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "call_ETC_L1_QP (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using ControlSystems, LinearAlgebra, Kronecker, SparseArrays, JuMP, Ipopt, OSQP, Plots\n",
    "const ETC_L1_QP_lib = \"./ETC_L1_QP.so\"\n",
    "function call_ETC_L1_QP(L_Q_inv::Array{Float64,2},V::Array{Float64,2}, c::Array{Float64,1}, G::Array{Float64,2}, g::Array{Float64,1}, rho::Array{Float64,1}, epsilon::Float64, m::Int, n::Int)\n",
    "    y = Array{Float64,1}(undef,m)\n",
    "    run_time = Array{Float64,}(undef,1)\n",
    "    ccall(\n",
    "        (:ETC_L1_QP, ETC_L1_QP_lib),\n",
    "        Cvoid,\n",
    "        (Ptr{Cdouble}, Ptr{Cdouble}, Ptr{Cdouble}, Ptr{Cdouble}, Ptr{Cdouble}, Ptr{Cdouble}, Cdouble, Cint, Cint, Ptr{Cdouble}, Ptr{Cdouble}),\n",
    "        L_Q_inv, V, c, G, g, rho, epsilon, m, n, y, run_time\n",
    "    )\n",
    "    return y, run_time    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ts = 0.05\n",
    "NSim = 200\n",
    "Np = 20\n",
    "\n",
    "# Define the continuous-time model\n",
    "Ac = [-0.0151 -60.5651 0 -32.174;\n",
    "      -0.0001 -1.3411 0.9929 0;\n",
    "      0.00018 43.2541 -0.86939 0;\n",
    "      0 0 1 0]\n",
    "Bc = [-2.516 -13.136;\n",
    "     -0.1689 -0.2514;\n",
    "     -17.251 -1.5766;\n",
    "     0 0];\n",
    "Cc = [0 1 0 0;\n",
    "      0 0 0 1];\n",
    "Dc = [0 0;\n",
    "      0 0];\n",
    "sys = ss(Ac,Bc,Cc,Dc)\n",
    "model = c2d(sys, Ts)\n",
    "nx, nu = size(model.B)\n",
    "A_aug = [model.A model.B;\n",
    "         zeros(nu,nx) I(nu)]\n",
    "B_aug = [model.B;\n",
    "         I(nu)]\n",
    "C_aug = [model.C zeros(nu,nu)]\n",
    "\n",
    "# MPC-to-QP condense construction\n",
    "Wy = 10 * I(nu)\n",
    "Wdu = 0.1 * I(nu)\n",
    "AiB = B_aug\n",
    "BB = kron(I(Np),AiB)\n",
    "for i in 1:Np-1\n",
    "    AiB = A_aug * AiB\n",
    "    BB += kron(spdiagm(-i=>ones(Np-i)),AiB)\n",
    "end\n",
    "QQ = kron(I(Np), C_aug'*Wy*C_aug)\n",
    "RR = kron(I(Np), Wdu)\n",
    "Q = BB' * QQ * BB + RR\n",
    "Q = (Q+Q')/2\n",
    "\n",
    "E_x = [0 1 0 0 0 0;\n",
    "       0 0 0 1 0 0;\n",
    "       0 0 0 0 1 0;\n",
    "       0 0 0 0 0 1]\n",
    "G = [kron(I(Np), E_x)*BB; -kron(I(Np), E_x)*BB];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The wost-case computation of our ETC-L1-QP solver is 0.034774466000000004 seconds\n"
     ]
    }
   ],
   "source": [
    "# closed-loop simulation using mine L1-QP solver\n",
    "sleep(1)\n",
    "ref = [0.0; 10.0]\n",
    "x = [0; 5; 0; 0] # lies in an infeasible region\n",
    "u = zeros(nu)\n",
    "Ref_Hist = ref\n",
    "U_Hist = Matrix{Float64}(undef, 2, 0)\n",
    "Y_Hist = model.C*x\n",
    "Run_time_Hist = []\n",
    "for k in 1:NSim\n",
    "    if mod(k,100)==0\n",
    "        ref = [0.0; 0.0]\n",
    "    end\n",
    "    Ref_Hist = [Ref_Hist ref]\n",
    "    # finish uncompleted MPC-to-QP condense construction\n",
    "    x0 = [x; u]\n",
    "    ei = A_aug * x0\n",
    "    ee = ei\n",
    "    gg = E_x*ei\n",
    "    for i in 2:Np\n",
    "        ei = A_aug * ei\n",
    "        ee = [ee; ei]\n",
    "        gg = [gg; E_x*ei]\n",
    "    end\n",
    "    c = BB' * (QQ*ee - vec(repeat(C_aug'*Wy*ref, Np, 1)))\n",
    "    g = [vec(repeat([0.5;100;25;25],Np,1)) - gg; gg - vec(repeat([-0.5;-100;-25;-25],Np,1))]\n",
    "    # using our ETC-L1-QP solver\n",
    "    rho = vec(1000 * [repeat([1.0;1.0;10.0;10.0],Np,1); repeat([1.0;1.0;10.0;10.0],Np,1)])\n",
    "    Q_chol = cholesky(Q)\n",
    "    L_Q_inv = Matrix(inv(Q_chol.L))\n",
    "    V = G*L_Q_inv'\n",
    "    epsilon = 1e-6\n",
    "    dU, run_time = call_ETC_L1_QP(L_Q_inv, V, c, G, g, rho, epsilon, length(c), length(g))\n",
    "    Run_time_Hist = [Run_time_Hist; run_time]\n",
    "    # apply the first control input\n",
    "    u = u + dU[1:nu]\n",
    "    x = model.A * x + model.B * u\n",
    "    U_Hist = hcat(U_Hist, u)\n",
    "    Y_Hist = [Y_Hist model.C*x]\n",
    "end\n",
    "worst_case_computation_time = maximum(Run_time_Hist)\n",
    "println(\"The wost-case computation of our ETC-L1-QP solver is $worst_case_computation_time seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_layout = @layout [a b; c d]\n",
    "p = plot(layout = plot_layout)\n",
    "plot!(p, 0:NSim, Y_Hist[1,:], label=false, color=:red, linewidth=1,ylabel=\"y1\",subplot=1)\n",
    "plot!(p, 0:NSim, Y_Hist[2,:], label=false, color=:red, linewidth=1,ylabel=\"y2\",subplot=2)\n",
    "plot!(p, 0:NSim-1, U_Hist[1,:], label=false, color=:red, linewidth=1,ylabel=\"u1\",subplot=3)\n",
    "plot!(p, 0:NSim-1, U_Hist[2,:], label=false, color=:red, linewidth=1,ylabel=\"u2\",subplot=4)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The wost-case computation of IPOPT is 0.045530080795288086 seconds\n"
     ]
    }
   ],
   "source": [
    "# closed-loop simulation using Ipopt\n",
    "sleep(1)\n",
    "ref = [0.0; 10.0]\n",
    "x = [0; 5; 0; 0] # lies in an infeasible region\n",
    "u = zeros(nu)\n",
    "Ref_Hist = ref\n",
    "U_Hist = Matrix{Float64}(undef, 2, 0)\n",
    "Y_Hist = model.C*x\n",
    "Run_time_Hist_Ipopt_L1_QP = []\n",
    "for k in 1:NSim\n",
    "    if mod(k,100)==0\n",
    "        ref = [0.0; 0.0]\n",
    "    end\n",
    "    Ref_Hist = [Ref_Hist ref]\n",
    "    # finish uncompleted MPC-to-QP condense construction\n",
    "    x0 = [x; u]\n",
    "    ei = A_aug * x0\n",
    "    ee = ei\n",
    "    gg = E_x*ei\n",
    "    for i in 2:Np\n",
    "        ei = A_aug * ei\n",
    "        ee = [ee; ei]\n",
    "        gg = [gg; E_x*ei]\n",
    "    end\n",
    "    c = BB' * (QQ*ee - vec(repeat(C_aug'*Wy*ref, Np, 1)))\n",
    "    g = [vec(repeat([0.5;100;25;25],Np,1)) - gg; gg - vec(repeat([-0.5;-100;-25;-25],Np,1))]\n",
    "\n",
    "    # using Ipopt to solve L1-QP\n",
    "    rho = vec(1000 * [repeat([1.0;1.0;10.0;10.0],Np,1); repeat([1.0;1.0;10.0;10.0],Np,1)])\n",
    "    H = G*inv(Q)*G'\n",
    "    h = G*inv(Q)*c + g\n",
    "    model_0 = Model(Ipopt.Optimizer)\n",
    "    set_attribute(model_0, \"print_level\", 0)\n",
    "    @variable(model_0, 0.0 <= z[i=1:length(h)]<= rho[i])\n",
    "    @objective(model_0, Min, 0.5 * z' * H * z + h'*z)\n",
    "    optimize!(model_0)\n",
    "    z_Ipopt_L1_QP = [value(z[i]) for i in 1:length(h)]\n",
    "    dU = -inv(Q)*(c+G'*z_Ipopt_L1_QP)\n",
    "    sol_time_Ipopt_L1_QP = MOI.get(model_0, MOI.SolveTimeSec())\n",
    "    Run_time_Hist_Ipopt_L1_QP = [Run_time_Hist_Ipopt_L1_QP; sol_time_Ipopt_L1_QP]\n",
    "    # apply the first control input\n",
    "    u = u + dU[1:nu]\n",
    "    x = model.A * x + model.B * u\n",
    "    U_Hist = hcat(U_Hist, u)\n",
    "    Y_Hist = [Y_Hist model.C*x]\n",
    "end\n",
    "worst_case_computation_time_IPOPT = maximum(Run_time_Hist_Ipopt_L1_QP)\n",
    "println(\"The wost-case computation of IPOPT is $worst_case_computation_time_IPOPT seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_layout = @layout [a b; c d]\n",
    "p = plot(layout = plot_layout)\n",
    "plot!(p, 0:NSim, Y_Hist[1,:], label=false, color=:red, linewidth=1,ylabel=\"y1\",subplot=1)\n",
    "plot!(p, 0:NSim, Y_Hist[2,:], label=false, color=:red, linewidth=1,ylabel=\"y2\",subplot=2)\n",
    "plot!(p, 0:NSim-1, U_Hist[1,:], label=false, color=:red, linewidth=1,ylabel=\"u1\",subplot=3)\n",
    "plot!(p, 0:NSim-1, U_Hist[2,:], label=false, color=:red, linewidth=1,ylabel=\"u2\",subplot=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The wost-case computation of OSQP is 0.11281579 seconds\n"
     ]
    }
   ],
   "source": [
    "# closed-loop simulation using OSQP in L1-QP formulation\n",
    "sleep(1)\n",
    "ref = [0.0; 10.0]\n",
    "x = [0; 5; 0; 0] # lies in an infeasible region\n",
    "u = zeros(nu)\n",
    "Ref_Hist = ref\n",
    "U_Hist = Matrix{Float64}(undef, 2, 0)\n",
    "Y_Hist = model.C*x\n",
    "Run_time_Hist_OSQP_L1_QP = []\n",
    "prob = OSQP.Model()\n",
    "for k in 1:NSim\n",
    "    if mod(k,100)==0\n",
    "        ref = [0.0; 0.0]\n",
    "    end\n",
    "    Ref_Hist = [Ref_Hist ref]\n",
    "    # finish uncompleted MPC-to-QP condense construction\n",
    "    x0 = [x; u]\n",
    "    ei = A_aug * x0\n",
    "    ee = ei\n",
    "    gg = E_x*ei\n",
    "    for i in 2:Np\n",
    "        ei = A_aug * ei\n",
    "        ee = [ee; ei]\n",
    "        gg = [gg; E_x*ei]\n",
    "    end\n",
    "    c = BB' * (QQ*ee - vec(repeat(C_aug'*Wy*ref, Np, 1)))\n",
    "    g = [vec(repeat([0.5;100;25;25],Np,1)) - gg; gg - vec(repeat([-0.5;-100;-25;-25],Np,1))]\n",
    "    # using OSQP to solve L1-QP\n",
    "    rho = vec(1000 * [repeat([1.0;1.0;10.0;10.0],Np,1); repeat([1.0;1.0;10.0;10.0],Np,1)])\n",
    "    H = G*inv(Q)*G'\n",
    "    h = G*inv(Q)*c + g\n",
    "    OSQP.setup!(prob; P=sparse(H), q=h, A=sparse(Diagonal(ones(length(h)))),l=zeros(length(h)),u=rho, eps_abs=1e-6, eps_rel=1e-6, verbose=0)\n",
    "    res = OSQP.solve!(prob)\n",
    "    z_OSQP_L1_QP = res.x\n",
    "    dU = -inv(Q)*(c+G'*z_OSQP_L1_QP)\n",
    "    sol_time_OSQP_L1_QP = res.info.run_time\n",
    "    Run_time_Hist_OSQP_L1_QP = [Run_time_Hist_OSQP_L1_QP; sol_time_OSQP_L1_QP]\n",
    "    # apply the first control input\n",
    "    u = u + dU[1:nu]\n",
    "    x = model.A * x + model.B * u\n",
    "    U_Hist = hcat(U_Hist, u)\n",
    "    Y_Hist = [Y_Hist model.C*x]\n",
    "end\n",
    "worst_case_computation_time_OSQP = maximum(Run_time_Hist_OSQP_L1_QP)\n",
    "println(\"The wost-case computation of OSQP is $worst_case_computation_time_OSQP seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_layout = @layout [a b; c d]\n",
    "p = plot(layout = plot_layout)\n",
    "plot!(p, 0:NSim, Y_Hist[1,:], label=false, color=:red, linewidth=1,ylabel=\"y1\",subplot=1)\n",
    "plot!(p, 0:NSim, Y_Hist[2,:], label=false, color=:red, linewidth=1,ylabel=\"y2\",subplot=2)\n",
    "plot!(p, 0:NSim-1, U_Hist[1,:], label=false, color=:red, linewidth=1,ylabel=\"u1\",subplot=3)\n",
    "plot!(p, 0:NSim-1, U_Hist[2,:], label=false, color=:red, linewidth=1,ylabel=\"u2\",subplot=4)"
   ]
  }
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