{
"cells": [
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"function cls_solve(A,b,C,d) \n",
" m, n = size(A)\n",
" p, n = size(C)\n",
" G = A'*A # Gram matrix\n",
" KKT = [2*G C'; C zeros(p,p)] # KKT matrix \n",
" xzhat = KKT \\ [2*A'*b; d]\n",
" return xzhat[1:n,:]\n",
"end;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The objective function "
]
},
{
"attachments": {
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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"attachments": {
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}
},
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"attachments": {
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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"function lqr(A,B,C,x_init,x_des,T,rho) \n",
" n = size(A,1)\n",
" m = size(B,2)\n",
" p = size(C,1)\n",
" q = size(x_init,2)\n",
" Atil = [ kron(eye(T), C) zeros(p*T,m*(T-1)) ;\n",
" zeros(m*(T-1), n*T) sqrt(rho)*eye(m*(T-1)) ]\n",
" btil = zeros(p*T + m*(T-1), q)\n",
"\n",
" Ctil11 = [ kron(eye(T-1), A) zeros(n*(T-1),n) ] -\n",
" [ zeros(n*(T-1), n) eye(n*(T-1)) ]\n",
" Ctil12 = kron(eye(T-1), B)\n",
" Ctil21 = [eye(n) zeros(n,n*(T-1)); zeros(n,n*(T-1)) eye(n)] \n",
" Ctil22 = zeros(2*n,m*(T-1))\n",
" Ctil = [Ctil11 Ctil12; Ctil21 Ctil22]\n",
" dtil = [zeros(n*(T-1), q); x_init; x_des]\n",
" z = cls_solve(Atil,btil,Ctil,dtil)\n",
" x = [z[(i-1)*n+1:i*n,:] for i=1:T]\n",
" u = [z[n*T+(i-1)*m+1 : n*T+i*m, :] for i=1:T-1]\n",
" y = [C*xt for xt in x]\n",
" return x, u, y\n",
"end;"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"A = [ 0.855 1.161 0.667; \n",
" 0.015 1.073 0.053;\n",
" -0.084 0.059 1.022 ];\n",
"B = [-0.076; -0.139; 0.342 ];\n",
"C = [ 0.218 -3.597 -1.683 ];\n",
"n = 3; p = 1; m = 1;\n",
"x_init = [0.496; -0.745; 1.394];\n",
"x_des = zeros(n,1);"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T = 100;\n",
"yol = zeros(T,1);\n",
"Xol = [ x_init zeros(n, T-1) ]; \n",
"for k=1:T-1\n",
" Xol[:,k+1] = A*Xol[:,k];\n",
"end;\n",
"yol = C*Xol;\n",
"using Plots\n",
"plot(1:T, yol', legend = false)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.7738942551160483"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rho = 0.2;\n",
"T = 100;\n",
"x, u, y = lqr(A,B,C,x_init,x_des,T,rho) \n",
"J_input = norm(u)^2"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.782998646332306"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"J_output = norm(y)^2"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
" plot(1:T-1, vcat(u...), legend = false, xlabel=\"t\",\n",
"ylabel= \"u_t\")"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(1:T, vcat(y...), legend=false, xlabel = \"t\",\n",
"ylabel = \"y_t\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.6.4",
"language": "julia",
"name": "julia-0.6"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}