{ "cells": [ { "cell_type": "markdown", "id": "5298c815", "metadata": {}, "source": [ "# 13 — Quadratic-impact control\n", "\n", "Doc page: [quadratic_impact_control.rst](../../docs/source/algorithms/quadratic_impact_control.rst).\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "2784f52d", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:05:39.068751Z", "iopub.status.busy": "2026-05-12T14:05:39.068281Z", "iopub.status.idle": "2026-05-12T14:05:39.780916Z", "shell.execute_reply": "2026-05-12T14:05:39.779456Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from optimizr import _core as opt\n", "plt.rcParams['figure.figsize'] = (8.5, 4.5)\n", "plt.rcParams['figure.dpi'] = 110\n", "plt.rcParams['axes.grid'] = True\n", "plt.rcParams['grid.alpha'] = 0.3\n" ] }, { "cell_type": "markdown", "id": "c41c1654", "metadata": {}, "source": [ "## Cellule 1 — Riccati générique sur un horizon fini\n", "\n", "**Théorème (HJB quadratique 1-D).** Pour $dq_t = u_t\\,dt + \\sigma\\,dW_t$\n", "et coût $L(q, u) = \\gamma u^2 + \\varphi q^2$, $g(q) = A q^2$, la\n", "fonction valeur est $V(t, q) = h(t) q^2$ avec\n", "$$h'(t) = h(t)^2 / \\gamma - \\varphi,\\qquad h(T) = A.$$\n", "Le feedback optimal est $u^*(t) = -(h(t)/\\gamma)\\,q(t)$.\n", "\n", "**Équation pivot.** Pour $\\gamma = \\varphi = A = 1$, le point fixe\n", "est $h^* = 1$ (car $h^2 - 1 = 0 \\Rightarrow h = 1$).\n", "\n", "**Ce que la cellule vérifie.** Le primitive\n", "`quadratic_impact_control_py(gamma=1, phi=1, A=1, T, n)` retourne\n", "$h(t) \\equiv 1$ et donc un gain de feedback unitaire.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "ea45dc8d", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:05:39.784224Z", "iopub.status.busy": "2026-05-12T14:05:39.783876Z", "iopub.status.idle": "2026-05-12T14:05:40.235857Z", "shell.execute_reply": "2026-05-12T14:05:40.234066Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max |h(t) - 1| = 0.000e+00\n", "Feedback gain : k(0) = 1.0000, k(T) = 1.0000\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "res = opt.quadratic_impact_control_py(gamma=1.0, phi=1.0,\n", " a_terminal=1.0,\n", " t_horizon=0.5, n_steps=500)\n", "ts = np.array(res['time_grid'])\n", "h = np.array(res['h'])\n", "k = np.array(res['feedback_gain'])\n", "\n", "err = float(np.max(np.abs(h - 1.0)))\n", "print(f\"max |h(t) - 1| = {err:.3e}\")\n", "print(f\"Feedback gain : k(0) = {k[0]:.4f}, k(T) = {k[-1]:.4f}\")\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(ts, h, lw=2, label=r'$h(t)$')\n", "ax.plot(ts, k, '--', lw=2, label=r'$k(t) = h(t)/\\gamma$')\n", "ax.axhline(1.0, ls=':', color='gray', alpha=0.6, label='point fixe = 1')\n", "ax.set_xlabel('t'); ax.set_ylabel('value')\n", "ax.set_title(\"Riccati quadratique scalaire\")\n", "ax.legend()\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "32009801", "metadata": {}, "source": [ "**Résultat attendu.** $h(t) \\equiv 1$ à précision machine.\n", "\n", "**Lecture du graphique.** Lignes plates à 1.\n", "\n", "**Conclusion.** Le primitive est validé sur le point fixe analytique.\n" ] }, { "cell_type": "markdown", "id": "ad7c6258", "metadata": {}, "source": [ "## Cellule 2 — Étude paramétrique : pénalisation $\\varphi$\n", "\n", "**Théorème.** Le point fixe $h^* = \\sqrt{\\gamma \\varphi}$ croît\n", "avec $\\varphi$.\n", "\n", "**Équation pivot.**\n", "$$h^* = \\sqrt{\\gamma \\varphi},\n", " \\qquad k^* = h^*/\\gamma = \\sqrt{\\varphi/\\gamma}.$$\n", "\n", "**Ce que la cellule vérifie.** Sweep $\\varphi \\in \\{0.1, 1, 4, 10\\}$ :\n", "$h(0)$ s'aligne sur $\\sqrt{\\varphi}$ pour $\\gamma = 1$.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "06bd916e", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:05:40.239729Z", "iopub.status.busy": "2026-05-12T14:05:40.239404Z", "iopub.status.idle": "2026-05-12T14:05:40.631944Z", "shell.execute_reply": "2026-05-12T14:05:40.630049Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "phi= 0.10 : h(0) = 0.3162, h* = 0.3162\n", "phi= 1.00 : h(0) = 1.0000, h* = 1.0000\n", "phi= 4.00 : h(0) = 2.0000, h* = 2.0000\n", "phi=10.00 : h(0) = 3.1623, h* = 3.1623\n" ] }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "phis = [0.1, 1.0, 4.0, 10.0]\n", "fig, ax = plt.subplots()\n", "for phi in phis:\n", " r = opt.quadratic_impact_control_py(1.0, phi, np.sqrt(phi),\n", " t_horizon=2.0, n_steps=500)\n", " h_arr = np.array(r['h'])\n", " h_star = np.sqrt(phi)\n", " ax.plot(r['time_grid'], h_arr,\n", " label=fr'$\\varphi = {phi}$, $h^*={h_star:.2f}$')\n", " print(f\"phi={phi:5.2f} : h(0) = {h_arr[0]:.4f}, h* = {h_star:.4f}\")\n", "ax.set_xlabel('t'); ax.set_ylabel('h(t)')\n", "ax.set_title(r'Sensibilité de $h$ au coefficient $\\varphi$')\n", "ax.legend()\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "bc4e642c", "metadata": {}, "source": [ "**Résultat attendu.** Plus $\\varphi$ est grand, plus le gain de\n", "feedback est élevé.\n", "\n", "**Lecture du graphique.** Quatre lignes plates à des hauteurs\n", "$\\sqrt{\\varphi}$.\n", "\n", "**Conclusion.** Le compromis état/contrôle est gouverné par le\n", "ratio $\\varphi/\\gamma$.\n" ] }, { "cell_type": "markdown", "id": "e89f285e", "metadata": {}, "source": [ "## Cellule 3 — Exemple concret : régulation autour d'un set-point\n", "\n", "**Modèle.** En boucle fermée $\\dot q = -k q$ avec $k = h/\\gamma$,\n", "la dynamique est $q(t) = q_0 e^{-kt}$. Cas pratique : régulateur\n", "thermique scalaire qui ramène la température vers $0$ (écart à la\n", "consigne).\n", "\n", "**Équation pivot.**\n", "$$q(t) = q_0\\,e^{-(h^*/\\gamma)\\,t}.$$\n", "\n", "**Ce que la cellule vérifie.** Pour différents $\\varphi$, on intègre\n", "$\\dot q = -k(t) q$ et on observe la vitesse de retour vers $0$.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "913f4685", "metadata": { "execution": { "iopub.execute_input": "2026-05-12T14:05:40.637900Z", "iopub.status.busy": "2026-05-12T14:05:40.637528Z", "iopub.status.idle": "2026-05-12T14:05:41.242971Z", "shell.execute_reply": "2026-05-12T14:05:41.241582Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "phi=0.25 : q(T) = 0.2227\n", "phi=1.00 : q(T) = 0.0494\n", "phi=4.00 : q(T) = 0.0024\n" ] }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T, n_steps = 3.0, 600\n", "dt = T / n_steps\n", "q0 = 1.0\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "for phi in [0.25, 1.0, 4.0]:\n", " r = opt.quadratic_impact_control_py(1.0, phi, np.sqrt(phi),\n", " t_horizon=T, n_steps=n_steps)\n", " k = np.array(r['feedback_gain'])\n", " q = np.zeros(n_steps + 1); q[0] = q0\n", " for i in range(n_steps):\n", " q[i + 1] = q[i] - dt * k[i] * q[i]\n", " ts = np.array(r['time_grid'])\n", " axes[0].plot(ts, q, lw=2, label=fr'$\\varphi = {phi}$')\n", " axes[1].plot(ts, k, lw=2, label=fr'$\\varphi = {phi}$')\n", " print(f\"phi={phi:.2f} : q(T) = {q[-1]:.4f}\")\n", "axes[0].set_xlabel('t'); axes[0].set_ylabel('q(t)')\n", "axes[0].set_title(\"Écart à la consigne\")\n", "axes[0].legend()\n", "axes[1].set_xlabel('t'); axes[1].set_ylabel('k(t) (gain)')\n", "axes[1].set_title(\"Gain de feedback\")\n", "axes[1].legend()\n", "fig.tight_layout(); plt.show()\n" ] }, { "cell_type": "markdown", "id": "db02a95b", "metadata": {}, "source": [ "**Résultat attendu.** Plus $\\varphi$ est grand, plus $q$ retourne\n", "rapidement à $0$.\n", "\n", "**Lecture du graphique.** Décroissance exponentielle visible ; gain\n", "plat (régime stationnaire de la Riccati).\n", "\n", "**Conclusion.** Le primitive fournit le gain optimal pour tout\n", "problème linéaire-quadratique scalaire à pénalité d'impact.\n" ] } ], "metadata": { "kernelspec": { "display_name": "rhftlab", "language": "python", "name": "rhftlab" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.13" } }, "nbformat": 4, "nbformat_minor": 5 }