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"""Module D: Three-phase HPI control flow (Algorithm 1) — NN edition.
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Phase 1: Find admissible L0 with PD critic (NN-based).
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Phase 2: Homotopy contraction L_i -> 0 with safety constraint.
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Phase 3: Standard policy iteration on original system (L = 0).
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"""
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import copy
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import numpy as np
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import torch
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from .data_collector import DataCollector
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from .nn_models import check_lyapunov_decrease, check_positive_definite
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from .nn_trainer import NNTrainer
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class HPIController:
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"""Implements the three-phase Homotopy-Based Policy Iteration algorithm
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using neural network function approximators."""
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def __init__(self, J=1.0, mgl=1.0, R=1.0, 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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Args:
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J: Moment of inertia (default 1.0).
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mgl: Mass x gravity x length product (default 1.0).
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R: Control cost weight (default 1.0).
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pe_amplitude: PE signal amplitude scale (default 0.5).
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lr: Learning rate for Adam optimizer.
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epochs: Training epochs per HPI iteration.
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lambda_weight: L2 regularization coefficient.
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"""
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self.J = float(J)
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self.mgl = float(mgl)
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self.R = float(R)
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self.lr = float(lr)
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self.epochs = int(epochs)
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self.lambda_weight = float(lambda_weight)
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self.pe_amplitude = float(pe_amplitude)
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self.collector = DataCollector(J=J, mgl=mgl)
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self.trainer = NNTrainer(R=R, lr=lr, epochs=epochs,
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lambda_weight=lambda_weight)
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# Override PE amplitude
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self.collector._scale = pe_amplitude / np.sum(
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np.abs(self.collector._a) + np.abs(self.collector._b)
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)
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# ═══════════════════════════════════════════════════════════════
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# Utility
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# ═══════════════════════════════════════════════════════════════
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def check_positive_definite(self, critic_nn=None, X_traj=None):
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"""Check if critic NN corresponds to a PD value function.
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Checks both Hessian at origin and V(x) positivity on trajectory.
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"""
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if critic_nn is None:
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critic_nn = self.trainer.critic_nn
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return check_positive_definite(critic_nn, X_traj=X_traj)
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def check_lyapunov_decrease(self, X, f_X):
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"""Check if current critic satisfies Lyapunov decrease on trajectory."""
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return check_lyapunov_decrease(self.trainer.critic_nn, X, f_X)
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def _compute_f_X(self, X):
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"""Drift dynamics f(x) = [x2, sin(x1)] on trajectory."""
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X = np.asarray(X)
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f_X = np.zeros_like(X)
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f_X[:, 0] = X[:, 1]
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f_X[:, 1] = np.sin(X[:, 0])
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return f_X
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def _hessian_info(self):
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"""Return (h11, h22, det) of the critic Hessian at origin for logging."""
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x0 = torch.zeros(1, 2, requires_grad=True)
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V0 = self.trainer.critic_nn(x0)
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grad_V = torch.autograd.grad(V0.sum(), x0, create_graph=True)[0]
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h11 = torch.autograd.grad(grad_V[0, 0], x0, retain_graph=True)[0][0, 0].item()
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h22 = torch.autograd.grad(grad_V[0, 1], x0, retain_graph=True)[0][0, 1].item()
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h12 = torch.autograd.grad(grad_V[0, 0], x0, retain_graph=True)[0][0, 1].item()
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det = h11 * h22 - h12 ** 2
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return h11, h22, det
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# ═══════════════════════════════════════════════════════════════
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# Phase 1: Find L0 — scan ALL L values, pick best loss
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# ═══════════════════════════════════════════════════════════════
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def phase_one_find_L0(self, x0, T, dt, L_start=0.1, L_step=0.5, L_max=20.0,
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verbose=False):
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"""Find admissible L0 by scanning all L values and picking the best.
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Unlike the polynomial version which returns at the FIRST PD L,
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this scans ALL L values and chooses the one with lowest Bellman
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residual loss AND positive-definite critic. This ensures Phase 2
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starts from the best possible critic.
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Args:
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x0: Initial state (2,).
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T: Simulation duration.
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dt: Time step.
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L_start: Starting L value.
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L_step: Increment step.
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L_max: Maximum L value before failure.
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verbose: If True, print progress.
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Returns:
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tuple: (L0, critic_sd, actor_sd, results_dict).
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Raises:
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RuntimeError: If no admissible L is found below L_max.
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"""
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L_values = []
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L = L_start
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while L <= L_max:
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L_values.append(L)
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L += L_step
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if not L_values:
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raise RuntimeError("No L values to try (L_start > L_max)")
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# Collect ONE shared trajectory with PE-only control (no actor)
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# for training at all L values.
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def u_func(t, x):
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return self.collector.pe_signal(t)
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t, X, U = self.collector.collect_trajectory(x0, T, dt, u_func)
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f_X = self._compute_f_X(X)
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best_L = None
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best_loss = float('inf')
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best_critic_sd = None
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best_actor_sd = None
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best_info = None
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for L in L_values:
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if verbose:
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print(f" Phase 1: trying L={L:.2f}...", flush=True)
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# Fresh trainer for each L
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trainer = NNTrainer(R=self.R, lr=self.lr, epochs=self.epochs,
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lambda_weight=self.lambda_weight)
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result = trainer.train_one_iteration(t, X, U, L, prev_actor=None, dt=dt)
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loss = result['loss_c']
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pd = check_positive_definite(trainer.critic_nn, X_traj=X)
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lyap = check_lyapunov_decrease(trainer.critic_nn, X, f_X)
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if verbose:
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h11, h22, det = self._hessian_info_via_trainer(trainer)
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print(f" loss={loss:.4e} PD={pd} lyap={lyap:.3f} "
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f"H=[{h11:.4f},{h22:.4f}] det={det:.4e}", flush=True)
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# Only consider PD critics; pick lowest loss
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if pd and loss < best_loss:
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best_L = L
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best_loss = loss
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best_critic_sd = {k: v.clone() for k, v in trainer.critic_nn.state_dict().items()}
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best_actor_sd = {k: v.clone() for k, v in trainer.actor_nn.state_dict().items()}
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best_info = {'loss': loss, 'lyap': lyap, 'mse': result['mse_c']}
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if best_L is None:
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raise RuntimeError(
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f"Phase 1 failed: no admissible L found up to L_max={L_max}. "
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f"Try increasing L_max or adjusting training parameters."
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)
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if verbose:
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print(f" Phase 1: selected L0={best_L:.2f} (loss={best_loss:.4e})",
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flush=True)
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# Load best weights into main trainer
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self.trainer.critic_nn.load_state_dict(best_critic_sd)
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self.trainer.actor_nn.load_state_dict(best_actor_sd)
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return best_L, best_critic_sd, best_actor_sd, best_info
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def _hessian_info_via_trainer(self, trainer):
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"""Get Hessian info from a specific trainer instance."""
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x0 = torch.zeros(1, 2, requires_grad=True)
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V0 = trainer.critic_nn(x0)
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grad_V = torch.autograd.grad(V0.sum(), x0, create_graph=True)[0]
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h11 = torch.autograd.grad(grad_V[0, 0], x0, retain_graph=True)[0][0, 0].item()
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h22 = torch.autograd.grad(grad_V[0, 1], x0, retain_graph=True)[0][0, 1].item()
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h12 = torch.autograd.grad(grad_V[0, 0], x0, retain_graph=True)[0][0, 1].item()
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det = h11 * h22 - h12 ** 2
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return h11, h22, det
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# ═══════════════════════════════════════════════════════════════
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# Phase 2: Homotopy contraction
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# ═══════════════════════════════════════════════════════════════
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def _compute_safe_alpha(self, X, prev_actor, L, gamma=0.1):
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"""Compute safe homotopy step alpha via inequality constraint."""
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x_tensor = torch.tensor(X, dtype=torch.float32, requires_grad=True)
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V = self.trainer.critic_nn(x_tensor)
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grad_V = torch.autograd.grad(V.sum(), x_tensor, create_graph=False)[0]
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dot_V = (grad_V * x_tensor).sum(dim=1).detach().numpy() # (M,)
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Q = X[:, 0] ** 2 + X[:, 1] ** 2 # (M,)
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if prev_actor is not None:
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with torch.no_grad():
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u_old = prev_actor(torch.tensor(X, dtype=torch.float32)).numpy()
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else:
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u_old = np.zeros(len(X))
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with torch.no_grad():
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u_new = self.trainer.actor_nn(torch.tensor(X, dtype=torch.float32)).numpy()
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gamma_c = 1.0 - gamma
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rhs = gamma_c * (Q + self.R * u_new ** 2) + self.R * (u_old - u_new) ** 2
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lhs = gamma_c * Q
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eps = 1e-10
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lower_candidates = []
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upper_candidates = []
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for k in range(len(dot_V)):
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d = dot_V[k]
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if d > eps:
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lower_candidates.append(lhs[k] / d)
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upper_candidates.append(rhs[k] / d)
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if not lower_candidates or not upper_candidates:
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return None
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alpha_lo = max(lower_candidates)
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alpha_hi = min(upper_candidates)
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if alpha_lo <= alpha_hi and alpha_hi > 0:
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return min(alpha_hi, L)
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return None
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def phase_two_contraction(self, x0, T, dt, L0, actor_sd_init, critic_sd_init,
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gamma=0.1, max_iter=50, verbose=False):
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"""Contract homotopy parameter L to zero via safety-constrained steps.
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Returns:
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tuple: (actor_sd, critic_sd, history).
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"""
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L = L0
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self.trainer.critic_nn.load_state_dict(critic_sd_init)
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self.trainer.actor_nn.load_state_dict(actor_sd_init)
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self.trainer.reset_optimizer()
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best_actor_sd = {k: v.clone() for k, v in actor_sd_init.items()}
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best_critic_sd = {k: v.clone() for k, v in critic_sd_init.items()}
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reject_streak = 0
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history = [(L, 0.0, True)] # (L, loss, PD)
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for iteration in range(max_iter):
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if verbose:
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print(f" Phase 2 iter {iteration}: L={L:.4f}", flush=True)
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prev_actor = self.trainer.copy_actor()
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def u_func(t, x):
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pe = self.collector.pe_signal(t)
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u_policy = self.trainer.compute_u_hat(x)
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return pe + u_policy
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t, X, U = self.collector.collect_trajectory(x0, T, dt, u_func)
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f_X = self._compute_f_X(X)
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# Fresh optimizer per iteration
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self.trainer.reset_optimizer()
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result = self.trainer.train_one_iteration(t, X, U, L, prev_actor, dt)
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pd_new = check_positive_definite(self.trainer.critic_nn, X_traj=X)
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alpha = self._compute_safe_alpha(X, prev_actor, L, gamma)
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if alpha is None:
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alpha = L * 0.2
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if pd_new:
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best_actor_sd = {k: v.clone() for k, v in self.trainer.actor_nn.state_dict().items()}
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best_critic_sd = {k: v.clone() for k, v in self.trainer.critic_nn.state_dict().items()}
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reject_streak = 0
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if verbose:
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lyap = check_lyapunov_decrease(self.trainer.critic_nn, X, f_X)
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print(f" alpha={alpha:.4f} loss={result['loss_c']:.4e} "
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f"lyap={lyap:.3f} PD", flush=True)
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else:
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self.trainer.actor_nn.load_state_dict(best_actor_sd)
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self.trainer.critic_nn.load_state_dict(best_critic_sd)
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reject_streak += 1
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if verbose:
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print(f" alpha={alpha:.4f} loss={result['loss_c']:.4e} "
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f"not PD (reject streak={reject_streak})", flush=True)
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L = max(0.0, L - alpha)
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history.append((L, result['loss_c'], pd_new))
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if L < 1e-14:
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if verbose:
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print(" L reached 0, Phase 2 complete", flush=True)
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break
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if reject_streak > 15:
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if verbose:
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print(" >15 consecutive rejections, stopping Phase 2", flush=True)
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break
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return best_actor_sd, best_critic_sd, history
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# ═══════════════════════════════════════════════════════════════
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# Phase 3: Standard policy iteration
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# ═══════════════════════════════════════════════════════════════
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def phase_three_pi(self, x0, T, dt, actor_sd_init, critic_sd_init,
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epsilon=1e-6, max_iter=30, verbose=False):
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"""Standard policy iteration on the original system (L = 0).
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Returns:
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tuple: (actor_sd, critic_sd, converged, history).
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"""
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self.trainer.actor_nn.load_state_dict(actor_sd_init)
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self.trainer.critic_nn.load_state_dict(critic_sd_init)
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self.trainer.reset_optimizer()
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prev_loss = float('inf')
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converged = False
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history = []
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for iteration in range(max_iter):
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if verbose:
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print(f" Phase 3 iter {iteration}", flush=True)
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prev_actor = self.trainer.copy_actor()
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def u_func(t, x):
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pe = self.collector.pe_signal(t)
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u_policy = self.trainer.compute_u_hat(x)
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u_policy = np.clip(u_policy, -5.0, 5.0)
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return pe + u_policy
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t, X, U = self.collector.collect_trajectory(x0, T, dt, u_func)
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self.trainer.reset_optimizer()
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result = self.trainer.train_one_iteration(t, X, U, 0.0, prev_actor, dt)
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loss = result['loss_c']
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history.append(loss)
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pd = check_positive_definite(self.trainer.critic_nn, X_traj=X)
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if verbose:
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f_X = self._compute_f_X(X)
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lyap = check_lyapunov_decrease(self.trainer.critic_nn, X, f_X)
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print(f" loss={loss:.4e} PD={pd} lyap={lyap:.3f}", flush=True)
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if abs(prev_loss - loss) < epsilon:
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converged = True
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break
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prev_loss = loss
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if loss > 1e6 or not np.isfinite(loss):
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break
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actor_sd = {k: v.clone() for k, v in self.trainer.actor_nn.state_dict().items()}
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critic_sd = {k: v.clone() for k, v in self.trainer.critic_nn.state_dict().items()}
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return actor_sd, critic_sd, converged, history
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# ═══════════════════════════════════════════════════════════════
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# Full pipeline
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# ═══════════════════════════════════════════════════════════════
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def run(self, x0=None, T=10.0, dt=0.01,
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L_start=0.1, L_step=0.5, L_max=20.0,
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gamma=0.1, epsilon=1e-6, verbose=True):
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"""Run the full three-phase HPI algorithm.
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Returns:
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dict: Results containing:
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- phase1_L0, phase1_critic_sd, phase1_actor_sd, phase1_info
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- phase2_history, phase2_actor_sd, phase2_critic_sd
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- phase3_actor_sd, phase3_critic_sd, phase3_converged, phase3_history
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"""
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if x0 is None:
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x0 = np.array([0.5, 0.0])
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results = {}
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# ── Phase 1: Find L0 ──
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L0, critic_sd1, actor_sd1, info1 = self.phase_one_find_L0(
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x0, T, dt, L_start, L_step, L_max, verbose=verbose)
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results["phase1_L0"] = L0
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results["phase1_critic_sd"] = critic_sd1
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results["phase1_actor_sd"] = actor_sd1
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results["phase1_info"] = info1
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# ── Phase 2: Homotopy contraction ──
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actor_sd2, critic_sd2, hist2 = self.phase_two_contraction(
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x0, T, dt, L0, actor_sd1, critic_sd1, gamma=gamma, verbose=verbose)
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results["phase2_actor_sd"] = actor_sd2
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results["phase2_critic_sd"] = critic_sd2
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results["phase2_history"] = hist2
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# ── Phase 3: Policy iteration ──
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actor_sd3, critic_sd3, converged, hist3 = self.phase_three_pi(
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x0, T, dt, actor_sd2, critic_sd2, epsilon, verbose=verbose)
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results["phase3_actor_sd"] = actor_sd3
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results["phase3_critic_sd"] = critic_sd3
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results["phase3_converged"] = converged
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results["phase3_history"] = hist3
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# Load final weights
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self.trainer.actor_nn.load_state_dict(actor_sd3)
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self.trainer.critic_nn.load_state_dict(critic_sd3)
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return results
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