bistable.ipynb 69.2 KB
Newer Older
YABO Agustin's avatar
YABO Agustin committed
1
2
3
4
5
6
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
YABO Agustin's avatar
YABO Agustin committed
7
8
9
    "# Bistable gene-regulatory networks\n",
    "\n",
    "## Model definition\n",
YABO Agustin's avatar
YABO Agustin committed
10
    "\n",
YABO Agustin's avatar
YABO Agustin committed
11
    "We consider the piecewise linear system defined in Filippov sense as in [Augier and Yabo (2021)][id1]. In synthetic biology, this model can represent a _genetic toggle switch_, a synthetic regulatory network designed by [Gardner et al. (2000)][id2] in the bacteria E. coli through two genes lacI and tetR mutually repressing each other. Dynamics is given by\n",
YABO Agustin's avatar
YABO Agustin committed
12
    "\n",
YABO Agustin's avatar
YABO Agustin committed
13
14
    "[id1]: https://hal.archives-ouvertes.fr/hal-03099681\n",
    "[id2]: https://pubmed.ncbi.nlm.nih.gov/10659857/\n",
YABO Agustin's avatar
YABO Agustin committed
15
    "\n",
YABO Agustin's avatar
YABO Agustin committed
16
    "$$\n",
YABO Agustin's avatar
YABO Agustin committed
17
18
19
20
    "\\left\\{ \\begin{array}{l}\n",
    "\\dot x_1 = -\\gamma_1 x_1 + u(t) k_1 s^{-}(x_2, \\theta_2), \\\\\n",
    "\\dot x_2 = -\\gamma_1 x_2 + u(t)k_2 s^{-}(x_1, \\theta_1),\n",
    "\\end{array}\n",
21
    "\\right.\n",
YABO Agustin's avatar
YABO Agustin committed
22
    "$$\n",
YABO Agustin's avatar
YABO Agustin committed
23
24
25
    "\n",
    "where for $j\\in \\{1,2\\}$, $x_j\\in \\mathbb{R}$, and for $\\theta\\in \\mathbb{R}$, $s^{-}(\\cdot,\\theta):\\mathbb{R}\\to \\mathbb{R}$ is such that\n",
    "\n",
YABO Agustin's avatar
YABO Agustin committed
26
    "$$\n",
YABO Agustin's avatar
YABO Agustin committed
27
28
29
30
    "    s^{-}(x,\\theta)= \\left\\{ \\begin{array}{ll}\n",
    "    1 & \\textit{if } x < \\theta, \\\\\n",
    "    0 & \\textit{if } x > \\theta,\n",
    "    \\end{array} \\right.\n",
YABO Agustin's avatar
YABO Agustin committed
31
    "$$\n",
YABO Agustin's avatar
YABO Agustin committed
32
33
34
    "\n",
    "and the control $u(\\cdot) \\in L^\\infty ([0,t_f],[u_{\\text{min}},u_{\\text{max}}])$, with $0<u_{\\text{min}}<1 \\leq u_{\\text{max}}$. Such system is piecewise linear in $\\mathbb{R}^2$ and, in particular, is linear in the regular domains\n",
    "\n",
YABO Agustin's avatar
YABO Agustin committed
35
    "$$\n",
YABO Agustin's avatar
YABO Agustin committed
36
37
38
39
40
41
    "\\begin{array}{ll}\n",
    "&B_{00}=\\left\\{(x_1,x_2)\\in \\mathbb{R}^2 \\mid 0<x_1<\\theta_1, \\ 0<x_2<\\theta_2\\right\\},\\\\\n",
    "& B_{01}=\\left\\{(x_1,x_2)\\in \\mathbb{R}^2 \\mid 0<x_1<\\theta_1, \\ \\theta_2<x_2<\\frac{k_2}{\\gamma_2}\\right\\},\\\\\n",
    "& B_{10}=\\left\\{(x_1,x_2)\\in \\mathbb{R}^2 \\mid \\theta_1<x_1<\\frac{k_1}{\\gamma_1}, \\ 0<x_2<\\theta_2\\right\\},\\\\\n",
    "&B_{11}=\\left\\{(x_1,x_2)\\in \\mathbb{R}^2 \\mid \\theta_1<x_1<\\frac{k_1}{\\gamma_1}, \\ \\theta_2<x_2<\\frac{k_2}{\\gamma_2}\\right\\}.\n",
    "\\end{array}\n",
YABO Agustin's avatar
YABO Agustin committed
42
    "$$\n",
YABO Agustin's avatar
YABO Agustin committed
43
    "\n",
44
45
    "The following image shows the dynamics for the open loop system (i.e. $u \\equiv 1$):\n",
    "\n",
YABO Agustin's avatar
YABO Agustin committed
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
    "<img src=\"openloop.png\" width=436 height=337>\n",
    "\n",
    "## Time-optimal control problem\n",
    "\n",
    "The optimal control problem involves minimizing the time of a state transfer from $B_{10}$ to $B_{01}$, and so is defined for the state $x(t) = (x_1(t),x_2(t))$ as \n",
    "\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "\t\\textit{minimize} \\ t_f  \\\\\n",
    "\t\\dot x = f(x),\\\\\n",
    " x(0) = x_0 \\in B_{10}, \\\\ x_1(t_f)\\in [0,\\theta_1), \\ x_2(t_f)=x_2^f > \\theta_2, \\\\ u(\\cdot) \\in [u_{\\text{min}},u_{\\text{max}}].\n",
    "\\end{array}\\right.\n",
    "$$\n",
    "\n",
    "with $f(x)$ being the right-hand side of the system previously introduced.\n",
YABO Agustin's avatar
YABO Agustin committed
61
    "\n",
YABO Agustin's avatar
YABO Agustin committed
62
    "## Problem regularization\n",
YABO Agustin's avatar
YABO Agustin committed
63
64
65
    "\n",
    "Bocop requires $s^-$ to be regularized to a smooth function. We then define, for $x\\in \\mathbb{R}$ and $k\\in \\mathbb{N}$, the Hill function\n",
    "\n",
YABO Agustin's avatar
YABO Agustin committed
66
67
68
    "$$\n",
    "\\delta(x_i,\\theta_i,k) = \\frac{\\theta_i^k}{x_i^k + \\theta_i^k},\n",
    "$$\n",
YABO Agustin's avatar
YABO Agustin committed
69
70
71
    "\n",
    "which can approximate $s^-$ for large values of $k$ and, when $k \\rightarrow \\infty$, meets\n",
    "\n",
YABO Agustin's avatar
YABO Agustin committed
72
    "$$\n",
YABO Agustin's avatar
YABO Agustin committed
73
74
75
76
77
    "\t\\lim_{k \\rightarrow \\infty} \\delta(x_i,\\theta_i,k) = \\left\\{ \\begin{array}{ll}\n",
    "\t1 & x_i < \\theta_i, \\\\\n",
    "\t0 & x_i > \\theta_i, \\\\\n",
    "\t1/2 & x_i = \\theta_i.\n",
    "\t\\end{array} \\right.\n",
YABO Agustin's avatar
YABO Agustin committed
78
    "$$\n",
YABO Agustin's avatar
YABO Agustin committed
79
    "\n",
YABO Agustin's avatar
YABO Agustin committed
80
    "System parameters are fixed to $\\gamma_1 = 1.2$, $\\gamma_2 = 2$, $\\theta_1 = 0.6$, $\\theta_2 = 0.4$ and $k_1 = k_2 = 1$, and control bounds are set to $u_{min}=0.5$ and $u_{max}=1.5$. Initial conditions are set to $x_1(0) = 0.8$, $x_2(0)=0.3$ and $x_2(t_f) = 0.7$. The parameter $k$ of the Hill function is set to $k = 200$.\n",
81
82
    "\n",
    "<font color=white>[Thumbnail](thumbnail.png)</font>"
YABO Agustin's avatar
YABO Agustin committed
83
84
85
86
   ]
  },
  {
   "cell_type": "code",
YABO Agustin's avatar
YABO Agustin committed
87
   "execution_count": 1,
YABO Agustin's avatar
YABO Agustin committed
88
89
90
91
92
93
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
YABO Agustin's avatar
YABO Agustin committed
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
      "\u001b[37m// +++DRAFT+++ This class implements the OCP functions\u001b[39;49;00m\r\n",
      "\u001b[37m// It derives from the generic class bocop3OCPBase\u001b[39;49;00m\r\n",
      "\u001b[37m// OCP functions are defined with templates since they will be called\u001b[39;49;00m\r\n",
      "\u001b[37m// from both the NLP solver (double arguments) and AD tool (ad_double arguments)\u001b[39;49;00m\r\n",
      "\u001b[37m//#pragma once\u001b[39;49;00m\r\n",
      "\r\n",
      "\u001b[36m#\u001b[39;49;00m\u001b[36minclude\u001b[39;49;00m \u001b[37m<OCP.h>\u001b[39;49;00m\u001b[36m\u001b[39;49;00m\r\n",
      "\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m <\u001b[34mtypename\u001b[39;49;00m \u001b[04m\u001b[32mVariable\u001b[39;49;00m>\r\n",
      "\u001b[36mvoid\u001b[39;49;00m OCP::finalCost(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m Variable *initial_state, \u001b[34mconst\u001b[39;49;00m Variable *final_state, \u001b[34mconst\u001b[39;49;00m Variable *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, Variable &final_cost)\r\n",
      "{\r\n",
      "  \u001b[37m// Minimize final time\u001b[39;49;00m\r\n",
      "  final_cost = initial_state[\u001b[34m2\u001b[39;49;00m];\r\n",
      "}\r\n",
      "\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m <\u001b[34mtypename\u001b[39;49;00m \u001b[04m\u001b[32mVariable\u001b[39;49;00m>\r\n",
      "\u001b[36mvoid\u001b[39;49;00m OCP::dynamics(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m Variable *state, \u001b[34mconst\u001b[39;49;00m Variable *control, \u001b[34mconst\u001b[39;49;00m Variable *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, Variable *state_dynamics)\r\n",
      "{\r\n",
      "\tVariable x1 = state[\u001b[34m0\u001b[39;49;00m];\r\n",
      "\tVariable x2 = state[\u001b[34m1\u001b[39;49;00m];\r\n",
      "\tVariable tf = state[\u001b[34m2\u001b[39;49;00m];\r\n",
      "\tVariable u  = control[\u001b[34m0\u001b[39;49;00m];\r\n",
      "\t\r\n",
      "\t\u001b[36mdouble\u001b[39;49;00m g1 = constants[\u001b[34m0\u001b[39;49;00m];\r\n",
      "\t\u001b[36mdouble\u001b[39;49;00m g2 = constants[\u001b[34m1\u001b[39;49;00m];\r\n",
      "\t\u001b[36mdouble\u001b[39;49;00m t1 = constants[\u001b[34m2\u001b[39;49;00m];\r\n",
      "\t\u001b[36mdouble\u001b[39;49;00m t2 = constants[\u001b[34m3\u001b[39;49;00m];\r\n",
      "\t\u001b[36mdouble\u001b[39;49;00m k  = constants[\u001b[34m4\u001b[39;49;00m];\r\n",
      "\t\r\n",
      "\tVariable delta1 = pow(t2,k)/(pow(t2,k) + pow(x2,k)); \u001b[37m// delta(x2,t2,k)\u001b[39;49;00m\r\n",
      "\tVariable delta2 = pow(t1,k)/(pow(t1,k) + pow(x1,k)); \u001b[37m// delta(x1,t1,k)\u001b[39;49;00m\r\n",
      "\r\n",
      "\tstate_dynamics[\u001b[34m0\u001b[39;49;00m] = -g1*x1 + u*delta1;\t\u001b[37m// x1dot\u001b[39;49;00m\r\n",
      "\tstate_dynamics[\u001b[34m1\u001b[39;49;00m] = -g2*x2 + u*delta2;\t\u001b[37m// x2dot\u001b[39;49;00m\r\n",
      "\tstate_dynamics[\u001b[34m2\u001b[39;49;00m] = \u001b[34m0\u001b[39;49;00m;\t\t\t\u001b[37m// tf (constant)\u001b[39;49;00m\r\n",
      "\t\r\n",
      "\t\u001b[37m// Rescale the state\u001b[39;49;00m\r\n",
      "\t\u001b[34mfor\u001b[39;49;00m (\u001b[36msize_t\u001b[39;49;00m i=\u001b[34m0\u001b[39;49;00m; i<\u001b[34m2\u001b[39;49;00m; i++)\r\n",
      "\t\tstate_dynamics[i] *= tf;\r\n",
      "}\r\n",
      "\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m <\u001b[34mtypename\u001b[39;49;00m \u001b[04m\u001b[32mVariable\u001b[39;49;00m>\r\n",
      "\u001b[36mvoid\u001b[39;49;00m OCP::boundaryConditions(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m Variable *initial_state, \u001b[34mconst\u001b[39;49;00m Variable *final_state, \u001b[34mconst\u001b[39;49;00m Variable *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, Variable *boundary_conditions)\r\n",
      "{\r\n",
      "    boundary_conditions[\u001b[34m0\u001b[39;49;00m] = initial_state[\u001b[34m0\u001b[39;49;00m]; \u001b[37m// x1(0)\u001b[39;49;00m\r\n",
      "    boundary_conditions[\u001b[34m1\u001b[39;49;00m] = initial_state[\u001b[34m1\u001b[39;49;00m]; \u001b[37m// x2(0)\u001b[39;49;00m\r\n",
      "    boundary_conditions[\u001b[34m2\u001b[39;49;00m] = final_state[\u001b[34m0\u001b[39;49;00m];   \u001b[37m// x1(tf)\u001b[39;49;00m\r\n",
      "    boundary_conditions[\u001b[34m3\u001b[39;49;00m] = final_state[\u001b[34m1\u001b[39;49;00m];   \u001b[37m// x2(tf)\u001b[39;49;00m\r\n",
      "}\r\n",
      "\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m <\u001b[34mtypename\u001b[39;49;00m \u001b[04m\u001b[32mVariable\u001b[39;49;00m>\r\n",
      "\u001b[36mvoid\u001b[39;49;00m OCP::pathConstraints(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m Variable *state, \u001b[34mconst\u001b[39;49;00m Variable *control, \u001b[34mconst\u001b[39;49;00m Variable *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, Variable *path_constraints)\r\n",
      "{}\r\n",
      "\r\n",
      "\u001b[36mvoid\u001b[39;49;00m OCP::preProcessing()\r\n",
      "{}\r\n",
      "\r\n",
      "\u001b[37m// ///////////////////////////////////////////////////////////////////\u001b[39;49;00m\r\n",
      "\u001b[37m// explicit template instanciation for template functions, with double and double_ad \u001b[39;49;00m\r\n",
      "\u001b[37m// +++ could be in an included separate file ? \u001b[39;49;00m\r\n",
      "\u001b[37m// but needs to be done for aux functions too ? APPARENTLY NOT !\u001b[39;49;00m\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::finalCost<\u001b[36mdouble\u001b[39;49;00m>(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *initial_state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *final_state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, \u001b[36mdouble\u001b[39;49;00m &final_cost);\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::dynamics<\u001b[36mdouble\u001b[39;49;00m>(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *control, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, \u001b[36mdouble\u001b[39;49;00m *state_dynamics);\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::boundaryConditions<\u001b[36mdouble\u001b[39;49;00m>(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *initial_state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *final_state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, \u001b[36mdouble\u001b[39;49;00m *boundary_conditions);\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::pathConstraints<\u001b[36mdouble\u001b[39;49;00m>(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *control, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, \u001b[36mdouble\u001b[39;49;00m *path_constraints);\r\n",
      "\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::finalCost<double_ad>(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m double_ad *initial_state, \u001b[34mconst\u001b[39;49;00m double_ad *final_state, \u001b[34mconst\u001b[39;49;00m double_ad *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, double_ad &final_cost);\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::dynamics<double_ad>(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m double_ad *state, \u001b[34mconst\u001b[39;49;00m double_ad *control, \u001b[34mconst\u001b[39;49;00m double_ad *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, double_ad *state_dynamics);\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::boundaryConditions<double_ad>(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m double_ad *initial_state, \u001b[34mconst\u001b[39;49;00m double_ad *final_state, \u001b[34mconst\u001b[39;49;00m double_ad *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, double_ad *boundary_conditions);\r\n",
      "\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::pathConstraints<double_ad>(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m double_ad *state, \u001b[34mconst\u001b[39;49;00m double_ad *control, \u001b[34mconst\u001b[39;49;00m double_ad *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, double_ad *path_constraints);\r\n"
YABO Agustin's avatar
YABO Agustin committed
164
165
166
167
168
169
170
171
172
     ]
    }
   ],
   "source": [
    "!pygmentize problem.cpp"
   ]
  },
  {
   "cell_type": "code",
YABO Agustin's avatar
YABO Agustin committed
173
   "execution_count": 2,
YABO Agustin's avatar
YABO Agustin committed
174
175
176
177
178
179
180
181
182
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import bocop"
   ]
  },
  {
   "cell_type": "code",
YABO Agustin's avatar
YABO Agustin committed
183
   "execution_count": 3,
YABO Agustin's avatar
YABO Agustin committed
184
185
186
187
188
189
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
YABO Agustin's avatar
YABO Agustin committed
190
      "[EXEC] > ['cmake -DCMAKE_BUILD_TYPE=Debug -DPROBLEM_DIR=/opt/ct-gallery/gallery/examples/bistable -DCPP_FILE=problem.cpp  -DCMAKE_CXX_COMPILER=g++  /opt/ct-gallery/env/lib/python3.7/site-packages/bocop']\n",
YABO Agustin's avatar
YABO Agustin committed
191
192
193
194
      ">\t-- The C compiler identification is GNU 7.5.0\n",
      ">\t-- The CXX compiler identification is GNU 10.2.0\n",
      ">\t-- Detecting C compiler ABI info\n",
      ">\t-- Detecting C compiler ABI info - done\n",
YABO Agustin's avatar
YABO Agustin committed
195
      ">\t-- Check for working C compiler: /opt/ct-gallery/env/bin/x86_64-conda-linux-gnu-cc - skipped\n",
YABO Agustin's avatar
YABO Agustin committed
196
197
198
199
      ">\t-- Detecting C compile features\n",
      ">\t-- Detecting C compile features - done\n",
      ">\t-- Detecting CXX compiler ABI info\n",
      ">\t-- Detecting CXX compiler ABI info - done\n",
YABO Agustin's avatar
YABO Agustin committed
200
      ">\t-- Check for working CXX compiler: /usr/bin/g++ - skipped\n",
YABO Agustin's avatar
YABO Agustin committed
201
202
      ">\t-- Detecting CXX compile features\n",
      ">\t-- Detecting CXX compile features - done\n",
YABO Agustin's avatar
YABO Agustin committed
203
      ">\t-- Problem path: /opt/ct-gallery/gallery/examples/bistable\n",
YABO Agustin's avatar
YABO Agustin committed
204
205
206
207
      ">\t-- Using CPPAD found at /opt/ct-gallery/env/include/cppad/..\n",
      ">\t-- Using IPOPT found at /opt/ct-gallery/env/lib/libipopt.so\n",
      ">\t-- Found Python3: /opt/ct-gallery/env/bin/python3.7 (found version \"3.7.8\") found components: Interpreter Development Development.Module Development.Embed \n",
      ">\t-- Found SWIG: /opt/ct-gallery/env/bin/swig (found suitable version \"4.0.2\", minimum required is \"4\")  \n",
YABO Agustin's avatar
YABO Agustin committed
208
209
210
      ">\t-- Build type: Debug\n",
      ">\t-- Configuring done\n",
      ">\t-- Generating done\n",
YABO Agustin's avatar
YABO Agustin committed
211
212
      ">\t-- Build files have been written to: /opt/ct-gallery/gallery/examples/bistable/build\n",
      "[DONE] > ['cmake -DCMAKE_BUILD_TYPE=Debug -DPROBLEM_DIR=/opt/ct-gallery/gallery/examples/bistable -DCPP_FILE=problem.cpp  -DCMAKE_CXX_COMPILER=g++  /opt/ct-gallery/env/lib/python3.7/site-packages/bocop']\n",
YABO Agustin's avatar
YABO Agustin committed
213
214
215
216
217
218
219
220
221
222
223
224
      "[EXEC] > make\n",
      ">\tScanning dependencies of target bocop\n",
      ">\t[  3%] Building CXX object src/CMakeFiles/bocop.dir/AD/dOCPCppAD.cpp.o\n",
      ">\t[  7%] Building CXX object src/CMakeFiles/bocop.dir/DOCP/dOCP.cpp.o\n",
      ">\t[ 10%] Building CXX object src/CMakeFiles/bocop.dir/DOCP/dODE.cpp.o\n",
      ">\t[ 14%] Building CXX object src/CMakeFiles/bocop.dir/DOCP/dControl.cpp.o\n",
      ">\t[ 17%] Building CXX object src/CMakeFiles/bocop.dir/DOCP/dState.cpp.o\n",
      ">\t[ 21%] Building CXX object src/CMakeFiles/bocop.dir/DOCP/solution.cpp.o\n",
      ">\t[ 25%] Building CXX object src/CMakeFiles/bocop.dir/NLP/NLPSolverIpopt.cpp.o\n",
      ">\t[ 28%] Building CXX object src/CMakeFiles/bocop.dir/OCP/OCP.cpp.o\n",
      ">\t[ 32%] Building CXX object src/CMakeFiles/bocop.dir/tools/tools.cpp.o\n",
      ">\t[ 35%] Building CXX object src/CMakeFiles/bocop.dir/tools/tools_interpolation.cpp.o\n",
YABO Agustin's avatar
YABO Agustin committed
225
226
      ">\t[ 39%] Building CXX object src/CMakeFiles/bocop.dir/opt/ct-gallery/gallery/examples/bistable/problem.cpp.o\n",
      ">\t[ 42%] Linking CXX shared library /opt/ct-gallery/gallery/examples/bistable/libbocop.so\n",
YABO Agustin's avatar
YABO Agustin committed
227
228
      ">\t[ 42%] Built target bocop\n",
      ">\tScanning dependencies of target bocopwrapper_swig_compilation\n",
YABO Agustin's avatar
YABO Agustin committed
229
      ">\t[ 46%] Swig compile /opt/ct-gallery/env/lib/python3.7/site-packages/bocop/src/bocopwrapper.i for python\n",
YABO Agustin's avatar
YABO Agustin committed
230
231
232
      ">\tLanguage subdirectory: python\n",
      ">\tSearch paths:\n",
      ">\t   ./\n",
YABO Agustin's avatar
YABO Agustin committed
233
      ">\t   /opt/ct-gallery/env/include/python3.7m/\n",
YABO Agustin's avatar
YABO Agustin committed
234
235
236
237
238
      ">\t   AD/\n",
      ">\t   DOCP/\n",
      ">\t   NLP/\n",
      ">\t   OCP/\n",
      ">\t   tools/\n",
YABO Agustin's avatar
YABO Agustin committed
239
240
241
242
243
244
245
246
      ">\t   /opt/ct-gallery/env/include/cppad/../\n",
      ">\t   /opt/ct-gallery/env/include/coin/\n",
      ">\t   /opt/ct-gallery/env/include/python3.7m/\n",
      ">\t   /opt/ct-gallery/env/lib/python3.7/site-packages/bocop/src/AD/\n",
      ">\t   /opt/ct-gallery/env/lib/python3.7/site-packages/bocop/src/DOCP/\n",
      ">\t   /opt/ct-gallery/env/lib/python3.7/site-packages/bocop/src/NLP/\n",
      ">\t   /opt/ct-gallery/env/lib/python3.7/site-packages/bocop/src/OCP/\n",
      ">\t   /opt/ct-gallery/env/lib/python3.7/site-packages/bocop/src/tools/\n",
YABO Agustin's avatar
YABO Agustin committed
247
      ">\t   ./swig_lib/python/\n",
YABO Agustin's avatar
YABO Agustin committed
248
      ">\t   /opt/ct-gallery/env/share/swig/4.0.2/python/\n",
YABO Agustin's avatar
YABO Agustin committed
249
      ">\t   ./swig_lib/\n",
YABO Agustin's avatar
YABO Agustin committed
250
      ">\t   /opt/ct-gallery/env/share/swig/4.0.2/\n",
YABO Agustin's avatar
YABO Agustin committed
251
252
253
254
255
256
257
258
259
      ">\tPreprocessing...\n",
      ">\tStarting language-specific parse...\n",
      ">\tProcessing types...\n",
      ">\tC++ analysis...\n",
      ">\tProcessing nested classes...\n",
      ">\tGenerating wrappers...\n",
      ">\t[ 46%] Built target bocopwrapper_swig_compilation\n",
      ">\tScanning dependencies of target bocopwrapper\n",
      ">\t[ 50%] Building CXX object src/CMakeFiles/bocopwrapper.dir/CMakeFiles/bocopwrapper.dir/bocopwrapperPYTHON_wrap.cxx.o\n",
YABO Agustin's avatar
YABO Agustin committed
260
261
      ">\t[ 53%] Linking CXX shared module /opt/ct-gallery/gallery/examples/bistable/_bocopwrapper.so\n",
      ">\t-- Moving python modules to /opt/ct-gallery/gallery/examples/bistable\n",
YABO Agustin's avatar
YABO Agustin committed
262
263
264
265
266
267
268
269
270
271
272
273
      ">\t[ 53%] Built target bocopwrapper\n",
      ">\tScanning dependencies of target bocopApp\n",
      ">\t[ 57%] Building CXX object src/CMakeFiles/bocopApp.dir/AD/dOCPCppAD.cpp.o\n",
      ">\t[ 60%] Building CXX object src/CMakeFiles/bocopApp.dir/DOCP/dOCP.cpp.o\n",
      ">\t[ 64%] Building CXX object src/CMakeFiles/bocopApp.dir/DOCP/dODE.cpp.o\n",
      ">\t[ 67%] Building CXX object src/CMakeFiles/bocopApp.dir/DOCP/dControl.cpp.o\n",
      ">\t[ 71%] Building CXX object src/CMakeFiles/bocopApp.dir/DOCP/dState.cpp.o\n",
      ">\t[ 75%] Building CXX object src/CMakeFiles/bocopApp.dir/DOCP/solution.cpp.o\n",
      ">\t[ 78%] Building CXX object src/CMakeFiles/bocopApp.dir/NLP/NLPSolverIpopt.cpp.o\n",
      ">\t[ 82%] Building CXX object src/CMakeFiles/bocopApp.dir/OCP/OCP.cpp.o\n",
      ">\t[ 85%] Building CXX object src/CMakeFiles/bocopApp.dir/tools/tools.cpp.o\n",
      ">\t[ 89%] Building CXX object src/CMakeFiles/bocopApp.dir/tools/tools_interpolation.cpp.o\n",
YABO Agustin's avatar
YABO Agustin committed
274
      ">\t[ 92%] Building CXX object src/CMakeFiles/bocopApp.dir/opt/ct-gallery/gallery/examples/bistable/problem.cpp.o\n",
YABO Agustin's avatar
YABO Agustin committed
275
      ">\t[ 96%] Building CXX object src/CMakeFiles/bocopApp.dir/main.cpp.o\n",
YABO Agustin's avatar
YABO Agustin committed
276
      ">\t[100%] Linking CXX executable /opt/ct-gallery/gallery/examples/bistable/bocopApp\n",
YABO Agustin's avatar
YABO Agustin committed
277
278
279
280
281
282
283
284
285
286
287
      ">\t[100%] Built target bocopApp\n",
      "[DONE] > make\n",
      "Done\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
YABO Agustin's avatar
YABO Agustin committed
288
     "execution_count": 3,
YABO Agustin's avatar
YABO Agustin committed
289
290
291
292
293
294
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem_path = \".\" # using local problem definition\n",
YABO Agustin's avatar
YABO Agustin committed
295
    "bocop.build(problem_path, cmake_options = '-DCMAKE_CXX_COMPILER=g++')"
YABO Agustin's avatar
YABO Agustin committed
296
297
298
299
300
301
302
303
304
305
306
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "State 0 and State 1 correspond to $x_1$ and $x_2$ respectively. State 2 represents the final time to minimize."
   ]
  },
  {
   "cell_type": "code",
YABO Agustin's avatar
YABO Agustin committed
307
   "execution_count": 4,
YABO Agustin's avatar
YABO Agustin committed
308
309
310
311
312
313
314
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
YABO Agustin's avatar
YABO Agustin committed
315
       "model_id": "6d62a4c4958c4c9994eab32d1b45b6be",
YABO Agustin's avatar
YABO Agustin committed
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=113, continuous_update=False, description='iteration', max=113), Output(…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Done\n"
     ]
YABO Agustin's avatar
YABO Agustin committed
332
333
334
335
336
337
338
339
340
341
342
343
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
YABO Agustin's avatar
YABO Agustin committed
344
345
346
    }
   ],
   "source": [
YABO Agustin's avatar
YABO Agustin committed
347
348
349
    "import matplotlib.pyplot as plt\n",
    "bocop.run(problem_path)\n",
    "plt.show()"
YABO Agustin's avatar
YABO Agustin committed
350
351
352
353
   ]
  },
  {
   "cell_type": "code",
YABO Agustin's avatar
YABO Agustin committed
354
   "execution_count": 5,
YABO Agustin's avatar
YABO Agustin committed
355
356
357
358
359
360
361
362
363
364
365
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading solution:  ./problem.sol\n"
     ]
    },
    {
     "data": {
YABO Agustin's avatar
YABO Agustin committed
366
      "image/png": "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\n",
YABO Agustin's avatar
YABO Agustin committed
367
      "text/plain": [
YABO Agustin's avatar
YABO Agustin committed
368
       "<Figure size 720x288 with 2 Axes>"
YABO Agustin's avatar
YABO Agustin committed
369
370
      ]
     },
YABO Agustin's avatar
YABO Agustin committed
371
372
373
     "metadata": {
      "needs_background": "light"
     },
YABO Agustin's avatar
YABO Agustin committed
374
375
376
377
378
379
380
381
382
383
384
385
386
387
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final time is 1.88756560904673\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "solution = bocop.readSolution(problem_path + \"/problem.sol\")\n",
YABO Agustin's avatar
YABO Agustin committed
388
389
390
    "tf = solution.state[2][0]; t = solution.time_steps*tf\n",
    "x1 = solution.state[0]; x2 = solution.state[1]\n",
    "u = solution.control[0]\n",
YABO Agustin's avatar
YABO Agustin committed
391
392
393
394
395
396
397
398
399
400
401
402
    "\n",
    "umin = 0.5\n",
    "umax = 1.5\n",
    "g1 = 1.4\n",
    "g2 = 1.8\n",
    "theta1 = 0.6\n",
    "theta2 = 0.4\n",
    "k1 = 1\n",
    "k2 = 1\n",
    "x1max = 0.9\n",
    "x2max = 0.8\n",
    "\n",
YABO Agustin's avatar
YABO Agustin committed
403
404
405
    "plt.figure(0, figsize=(10,4))\n",
    "plt.subplots_adjust(hspace=0.4, wspace=0.4)\n",
    "plt.subplot(121)\n",
YABO Agustin's avatar
YABO Agustin committed
406
407
408
409
410
411
    "ax = plt.gca()\n",
    "plt.xlabel('$x_1$'); plt.ylabel('$x_2$')\n",
    "ax.set_ylim(0.,x1max); ax.set_xlim(0.,x2max)\n",
    "xv = np.arange(0,theta1,0.01)\n",
    "sumax = k2/g2*umax - (k2/g2*umax - theta2)*((k1/g1*umax - xv)/((k1/g1*umax - theta1)))**(g2/g1)\n",
    "plt.plot(x1,x2,label='',zorder=3)\n",
YABO Agustin's avatar
YABO Agustin committed
412
    "plt.plot(xv,sumax,'--', label='$(S_{u_{max}})$',linewidth=1, color='grey')\n",
YABO Agustin's avatar
YABO Agustin committed
413
414
415
416
417
418
419
420
    "plt.legend()\n",
    "plt.xlim([0,theta1*1.8])\n",
    "ax.text(x1[0]+0.04, x2[0]-0.05, '$(x_1^0, x_2^0)$')\n",
    "plt.scatter([x1[0],x1[-1]],[x2[0],x2[-1]], zorder=3, s=20)\n",
    "plt.xticks([0, theta1], [0,'$\\\\theta_1$'])\n",
    "plt.yticks([0, theta2, x2[-1]], [0,'$\\\\theta_2$','$x_2^f$'])\n",
    "plt.grid(linestyle='dotted')\n",
    "\n",
YABO Agustin's avatar
YABO Agustin committed
421
422
423
424
425
426
427
428
    "plt.subplot(122)\n",
    "plt.plot(t[1:],u)\n",
    "plt.xlabel('Time'); plt.ylabel('$u$')\n",
    "plt.yticks([umin,1,umax], ['$u_{min}$', 1, '$u_{max}$'])\n",
    "plt.grid(linestyle='dotted')\n",
    "\n",
    "plt.show()\n",
    "\n",
YABO Agustin's avatar
YABO Agustin committed
429
430
431
432
433
    "print(\"Final time is \" + str(tf))"
   ]
  },
  {
   "cell_type": "code",
YABO Agustin's avatar
YABO Agustin committed
434
   "execution_count": 6,
YABO Agustin's avatar
YABO Agustin committed
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bocop returns status 0 with objective 1.888 and constraint violation 1.486e-14\n",
      "Costate at first time stage (t0+h/2):  [-2.21241861069235, 0.680215961376846, 0.99503700918767]\n",
      "Multipliers for initial conditions:  [-2.18337787e+00  6.68757718e-01  1.38521948e-12]\n"
     ]
    }
   ],
   "source": [
    "print(\"Bocop returns status {} with objective {:2.4g} and constraint violation {:2.4g}\".format(solution.status,solution.objective,solution.constraints))\n",
    "p0 = []\n",
    "for i in range(solution.dim_state):\n",
    "    p0.append(solution.costate[i][0])\n",
    "print(\"Costate at first time stage (t0+h/2): \",p0)\n",
    "print(\"Multipliers for initial conditions: \",solution.boundarycond_multipliers[0:solution.dim_state])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}