330 lines
12 KiB
Python
330 lines
12 KiB
Python
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"""HPI Control Validation — Inverted Pendulum (NN edition)
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Runs HPI algorithm (NN-based), compares with LQR baseline, validates in
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closed loop, outputs trajectories to CSV, and plots results.
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"""
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import os
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import numpy as np
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import pandas as pd
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import matplotlib
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matplotlib.use("TkAgg")
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import matplotlib.pyplot as plt
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from scipy.integrate import solve_ivp
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from scipy.linalg import solve_continuous_are
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from hpi.hpi_controller import HPIController
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plt.rcParams.update({
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"figure.figsize": (12, 8),
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"font.size": 12,
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"axes.titlesize": 14,
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"axes.labelsize": 13,
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"legend.fontsize": 11,
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"figure.dpi": 120,
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})
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OUTPUT_DIR = "output"
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os.makedirs(OUTPUT_DIR, exist_ok=True)
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# ═══════════════════════════════════════════════════════════════════
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# LQR Baseline
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# ═══════════════════════════════════════════════════════════════════
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def compute_lqr():
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"""Compute LQR solution for linearized inverted pendulum."""
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A = np.array([[0., 1.], [1., 0.]])
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B = np.array([[0.], [1.]])
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Q = np.eye(2)
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R = np.array([[1.]])
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P = solve_continuous_are(A, B, Q, R)
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K = (np.linalg.solve(R, B.T @ P)).ravel()
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return K
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# ═══════════════════════════════════════════════════════════════════
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# HPI
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# ═══════════════════════════════════════════════════════════════════
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def run_hpi():
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"""Run HPI algorithm, return controller and results."""
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print("=" * 60)
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print(" HPI Adaptive Optimal Control — Inverted Pendulum (NN)")
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print("=" * 60)
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controller = HPIController(
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J=1.0, mgl=1.0, R=1.0,
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pe_amplitude=0.5,
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lr=1e-3, epochs=500, lambda_weight=1e-6,
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)
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results = controller.run(
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x0=np.array([0.5, 0.0]),
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T=5.0,
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dt=0.05,
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L_start=0.1,
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L_step=1.0,
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L_max=10.0,
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gamma=0.1,
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epsilon=1e-3,
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)
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print(f"\n Phase 1 L0 = {results['phase1_L0']:.2f}")
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print(f" Phase 1 info: {results['phase1_info']}")
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print(f" Phase 2 iterations: {len(results['phase2_history'])}")
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print(f" Phase 3 converged: {results['phase3_converged']}")
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print(f" Phase 3 iterations: {len(results['phase3_history'])}")
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return controller, results
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# ═══════════════════════════════════════════════════════════════════
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# Simulation
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# ═══════════════════════════════════════════════════════════════════
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def simulate_closed_loop(controller, x0, T=5.0, n_points=500):
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"""Closed-loop simulation with HPI controller.
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Returns: t, X, U, V
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"""
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t_eval = np.linspace(0, T, n_points)
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def control(t, x):
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return controller.trainer.compute_u_hat(x)
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def ode(t, x):
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return controller.collector.dynamics(t, x, control)
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sol = solve_ivp(ode, (0, T), x0, method="RK45", t_eval=t_eval,
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rtol=1e-8, atol=1e-10)
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t = sol.t
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X = sol.y.T
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U = np.array([control(ti, xi) for ti, xi in zip(t, X)])
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V = controller.trainer.compute_V(X)
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return t, X, U, V
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def simulate_lqr_closed_loop(J, mgl, K, x0, T=5.0, n_points=500):
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"""Closed-loop simulation with LQR controller on nonlinear pendulum."""
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t_eval = np.linspace(0, T, n_points)
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def u_lqr(t, x):
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return float(-np.dot(K, x))
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def dynamics(t, x):
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return np.array([x[1], (mgl / J) * np.sin(x[0]) + (1.0 / J) * u_lqr(t, x)])
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sol = solve_ivp(dynamics, (0, T), x0, method="RK45", t_eval=t_eval,
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rtol=1e-8, atol=1e-10)
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t = sol.t
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X = sol.y.T
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U = np.array([u_lqr(ti, xi) for ti, xi in zip(t, X)])
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return t, X, U
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# ═══════════════════════════════════════════════════════════════════
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# I/O
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# ═══════════════════════════════════════════════════════════════════
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def save_csv(t, X, U, V, label):
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df = pd.DataFrame({"time": t, "x1": X[:, 0], "x2": X[:, 1], "u": U, "V": V})
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path = os.path.join(OUTPUT_DIR, f"trajectory_{label}.csv")
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df.to_csv(path, index=False)
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return path
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# ═══════════════════════════════════════════════════════════════════
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# Plotting
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# ═══════════════════════════════════════════════════════════════════
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def plot_results(all_data, controller, results):
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"""Plot state/control/value trajectories, phase portrait, convergence."""
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colors = ["#1f77b4", "#d62728", "#2ca02c", "#ff7f0e", "#9467bd", "#8c564b"]
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# ── Figure 1: State + Control + Value ──
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fig1, axes1 = plt.subplots(2, 2, figsize=(14, 10))
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for idx, (label, (t, X, U, V)) in enumerate(all_data.items()):
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c = colors[idx % len(colors)]
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axes1[0, 0].plot(t, X[:, 0], color=c, label=f"{label} (x0=[{X[0,0]:.1f},{X[0,1]:.1f}])")
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axes1[0, 1].plot(t, X[:, 1], color=c)
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axes1[1, 0].plot(t, U, color=c)
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axes1[1, 1].plot(t, V, color=c)
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axes1[0, 0].set_ylabel("$x_1$ (angle)")
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axes1[0, 0].set_title("State $x_1$")
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axes1[0, 0].legend(fontsize=9)
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axes1[0, 0].grid(True, alpha=0.3)
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axes1[0, 0].axhline(y=0, color="k", lw=0.5)
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axes1[0, 1].set_ylabel("$x_2$ (ang. velocity)")
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axes1[0, 1].set_title("State $x_2$")
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axes1[0, 1].grid(True, alpha=0.3)
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axes1[0, 1].axhline(y=0, color="k", lw=0.5)
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axes1[1, 0].set_xlabel("Time t (s)")
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axes1[1, 0].set_ylabel("$u$ (torque)")
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axes1[1, 0].set_title("Control Input")
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axes1[1, 0].grid(True, alpha=0.3)
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axes1[1, 1].set_xlabel("Time t (s)")
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axes1[1, 1].set_ylabel("$V(x)$")
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axes1[1, 1].set_title("Value Function")
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axes1[1, 1].grid(True, alpha=0.3)
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fig1.suptitle("HPI Optimal Control — Closed-Loop Validation", fontsize=15, fontweight="bold")
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plt.tight_layout()
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path1 = os.path.join(OUTPUT_DIR, "trajectories.png")
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fig1.savefig(path1, dpi=150, bbox_inches="tight")
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print(f" Plot saved: {path1}")
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# ── Figure 2: Phase Portrait ──
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fig2, ax2 = plt.subplots(figsize=(8, 8))
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for idx, (label, (t, X, U, V)) in enumerate(all_data.items()):
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c = colors[idx % len(colors)]
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ax2.plot(X[:, 0], X[:, 1], color=c, lw=1.5, label=label)
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ax2.scatter(X[0, 0], X[0, 1], color=c, s=80, marker="o", zorder=5)
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ax2.scatter(X[-1, 0], X[-1, 1], color=c, s=80, marker="x", zorder=5)
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ax2.set_xlabel("$x_1$ (angle)")
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ax2.set_ylabel("$x_2$ (angular velocity)")
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ax2.set_title("Phase Portrait")
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ax2.legend()
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ax2.grid(True, alpha=0.3)
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ax2.axhline(y=0, color="k", lw=0.5)
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ax2.axvline(x=0, color="k", lw=0.5)
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ax2.set_aspect("equal")
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path2 = os.path.join(OUTPUT_DIR, "phase_portrait.png")
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fig2.savefig(path2, dpi=150, bbox_inches="tight")
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print(f" Plot saved: {path2}")
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# ── Figure 3: Convergence ──
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fig3, axes3 = plt.subplots(1, 2, figsize=(14, 5))
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L_vals = [h[0] for h in results["phase2_history"]]
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axes3[0].plot(range(len(L_vals)), L_vals, "o-", color="#1f77b4", markersize=6)
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axes3[0].set_xlabel("Iteration")
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axes3[0].set_ylabel("L")
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axes3[0].set_title("Phase 2: Homotopy Contraction")
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axes3[0].grid(True, alpha=0.3)
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loss_history = results["phase3_history"]
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if len(loss_history) > 1:
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loss_diffs = [abs(loss_history[i] - loss_history[i - 1])
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for i in range(1, len(loss_history))]
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axes3[1].plot(range(len(loss_diffs)), loss_diffs, "o-", color="#d62728", markersize=6)
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axes3[1].set_yscale("log")
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axes3[1].set_xlabel("Iteration")
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axes3[1].set_ylabel("|loss change|")
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axes3[1].set_title("Phase 3: Loss Convergence (log)")
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axes3[1].grid(True, alpha=0.3)
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fig3.suptitle("HPI Convergence History", fontsize=14, fontweight="bold")
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plt.tight_layout()
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path3 = os.path.join(OUTPUT_DIR, "convergence.png")
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fig3.savefig(path3, dpi=150, bbox_inches="tight")
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print(f" Plot saved: {path3}")
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# ── Figure 4: Value function surface ──
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fig4, ax4 = plt.subplots(figsize=(8, 6))
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x1_g = np.linspace(-1.2, 1.2, 80)
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x2_g = np.linspace(-2.5, 2.5, 80)
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X1, X2 = np.meshgrid(x1_g, x2_g)
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Xf = np.column_stack([X1.ravel(), X2.ravel()])
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Vg = controller.trainer.compute_V(Xf).reshape(80, 80)
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vmin, vmax = max(Vg.min(), 1e-6), Vg.max()
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if vmax > vmin:
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levels = np.logspace(np.log10(vmin), np.log10(vmax), 20)
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cs = ax4.contourf(X1, X2, Vg, levels=levels, cmap="RdYlBu_r")
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ax4.contour(X1, X2, Vg, levels=levels[:8], colors="k", linewidths=0.3, alpha=0.5)
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fig4.colorbar(cs, ax=ax4, label="$V(x)$")
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for idx, (label, (t, X, U, V)) in enumerate(all_data.items()):
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ax4.plot(X[:, 0], X[:, 1], color=colors[idx % len(colors)], lw=1.5, label=label)
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ax4.set_xlabel("$x_1$ (angle)")
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ax4.set_ylabel("$x_2$ (ang. velocity)")
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ax4.set_title("Value Function with Phase Trajectories")
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ax4.legend(loc="upper left", fontsize=9)
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path4 = os.path.join(OUTPUT_DIR, "value_function.png")
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fig4.savefig(path4, dpi=150, bbox_inches="tight")
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print(f" Plot saved: {path4}")
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# ═══════════════════════════════════════════════════════════════════
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# Main
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# ═══════════════════════════════════════════════════════════════════
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def main():
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# ── LQR baseline ──
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print("=" * 60)
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print(" LQR Baseline (linearized pendulum)")
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print("=" * 60)
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K = compute_lqr()
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print(f" LQR gain K = {K}")
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# ── HPI ──
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controller, results = run_hpi()
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# ── Validation ──
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print("\n" + "=" * 60)
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print(" Closed-Loop Validation")
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print("=" * 60)
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test_cases = [
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("IC1_small_angle", np.array([0.5, 0.0])),
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("IC2_large_angle", np.array([0.9, 0.1])),
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("IC3_neg_angle", np.array([-0.7, -0.2])),
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("IC4_pos_vel", np.array([0.2, 1.5])),
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("IC5_neg_vel", np.array([-0.3, -1.2])),
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]
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all_data = {}
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summary = []
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for label, x0 in test_cases:
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# HPI
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t_h, X_h, U_h, V_h = simulate_closed_loop(controller, x0)
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n_hpi = np.linalg.norm(X_h[-1])
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# LQR
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t_l, X_l, U_l = simulate_lqr_closed_loop(controller.J, controller.mgl, K, x0)
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n_lqr = np.linalg.norm(X_l[-1])
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all_data[f"HPI_{label}"] = (t_h, X_h, U_h, V_h)
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save_csv(t_h, X_h, U_h, V_h, f"hpi_{label}")
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print(f" {label:20s} HPI: ||x(T)||={n_hpi:.2e} | LQR: ||x(T)||={n_lqr:.2e}")
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summary.append({
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"test_case": label, "x1_0": x0[0], "x2_0": x0[1],
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"hpi_norm_xT": n_hpi, "lqr_norm_xT": n_lqr,
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})
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df_s = pd.DataFrame(summary)
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sp = os.path.join(OUTPUT_DIR, "summary.csv")
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df_s.to_csv(sp, index=False)
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print(f"\n Summary: {sp}")
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print(f"\n LQR K = {K}")
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# ── Plot ──
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print("\n Generating plots...")
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plot_results(all_data, controller, results)
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print("\n Done! Output files in ./output/")
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if __name__ == "__main__":
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main()
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