Update controller_demo.ipynb

Author: MatthieuDarcy

docs/tutorials/control/controller_demo.ipynb

@@ -662,136 +662,6 @@
     "    \"Black-box sub-stepped SDE, partial observation, particle filter (PFConfig)\",\n",
     ")"
    ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "64e249ae",
-   "metadata": {},
-   "source": [
-    "## 7. A minimal black-box example\n",
-    "\n",
-    "Section 6's black box wraps a genuine sub-stepped SDE integration -- fairly involved. Here's the\n",
-    "smallest possible black box: a one-line nonlinear transition and a non-Gaussian observation, with\n",
-    "no solver calls at all.\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "x_{k+1} &= (x_k + \\eta_k)^2 + u_k, \\qquad \\eta_k \\sim \\mathcal{N}(0, \\sigma^2 I) \\\\\n",
-    "y_k &= H x_k + \\varepsilon_k, \\qquad \\varepsilon_k \\sim \\mathrm{Laplace}(0, b)\n",
-    "\\end{aligned}\n",
-    "$$\n",
-    "\n",
-    "The noise enters *inside* the square, so $x_{k+1}$ is non-Gaussian even though $\\eta_k$ itself is\n",
-    "simple Gaussian -- there's no `mean + additive noise` form to exploit, so the transition has to be\n",
-    "a black box again: a tiny class exposing only `.sample(key)`/`.shape()`, exactly like\n",
-    "`SubSteppedSDEStep` above, just without any sub-stepping.\n",
-    "\n",
-    "The observation noise is explicitly **non-Gaussian** (Laplace) to make the point that the\n",
-    "observation model isn't restricted to Gaussian noise either -- but note this one *can't* be a bare\n",
-    "`.sample()`-only black box like the transition: cuthbert's particle filter weights particles via\n",
-    "`observation_model(x, u, t).log_prob(y)`, so it needs a real `numpyro.distributions.Distribution`\n",
-    "with a working density, not just a sampler."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "id": "41a85aee",
-   "metadata": {
-    "execution": {
-     "iopub.execute_input": "2026-08-05T18:22:45.882623Z",
-     "iopub.status.busy": "2026-08-05T18:22:45.882561Z",
-     "iopub.status.idle": "2026-08-05T18:22:45.892487Z",
-     "shell.execute_reply": "2026-08-05T18:22:45.892168Z"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "class MinimalBlackBoxTransition:\n",
-    "    \"\"\"f(x, u, t_now, t_next) = (x + noise)^2 + u -- noise enters *inside*\n",
-    "    the square, so x_next is non-Gaussian even though the noise itself is\n",
-    "    simple Gaussian. Only .sample()/.shape() are exposed, same minimal\n",
-    "    contract as SubSteppedSDEStep above.\"\"\"\n",
-    "\n",
-    "    def __init__(self, x, u, noise_std):\n",
-    "        self._x, self._u, self._noise_std = x, u, noise_std\n",
-    "\n",
-    "    def sample(self, key):\n",
-    "        noise = self._noise_std * jr.normal(key, self._x.shape)\n",
-    "        return (self._x + noise) ** 2 + self._u\n",
-    "\n",
-    "    def shape(self):\n",
-    "        return self._x.shape\n",
-    "\n",
-    "\n",
-    "def minimal_black_box_transition(x, u, t_now, t_next):\n",
-    "    return MinimalBlackBoxTransition(x, u, noise_std=0.1)\n",
-    "\n",
-    "\n",
-    "def minimal_black_box_observation(x, u, t):\n",
-    "    # Laplace noise -- genuinely non-Gaussian, unlike every other observation\n",
-    "    # model in this notebook. Needs a real Distribution (not a bare .sample()\n",
-    "    # black box like the transition above): PF weights particles via\n",
-    "    # observation_model(x, u, t).log_prob(y).\n",
-    "    return dist.Independent(\n",
-    "        dist.Laplace(loc=jnp.eye(obs_dim_2d, state_dim_2d) @ x, scale=0.1), 1\n",
-    "    )\n",
-    "\n",
-    "\n",
-    "minimal_dynamics = DynamicalModel(\n",
-    "    initial_condition=dist.MultivariateNormal(\n",
-    "        jnp.array([3.0, 2.0]), 0.05 * jnp.eye(state_dim_2d)\n",
-    "    ),\n",
-    "    state_evolution=minimal_black_box_transition,\n",
-    "    observation_model=minimal_black_box_observation,\n",
-    "    control_dim=control_dim_2d,\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "id": "6e1d0eb3",
-   "metadata": {
-    "execution": {
-     "iopub.execute_input": "2026-08-05T18:22:45.893499Z",
-     "iopub.status.busy": "2026-08-05T18:22:45.893436Z",
-     "iopub.status.idle": "2026-08-05T18:22:46.526938Z",
-     "shell.execute_reply": "2026-08-05T18:22:46.526646Z"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "# Squaring the state each step is explosive -- no bounded control can cancel\n",
-    "# quadratic growth once x drifts away from 0, so this stays finite only for a\n",
-    "# short horizon (a handful of steps already overflows float32).\n",
-    "minimal_predict_times = jnp.arange(0.0, 0.3, 0.1)\n",
-    "\n",
-    "minimal_result = dsx.simulate(\n",
-    "    minimal_dynamics,\n",
-    "    rng_key=jr.PRNGKey(0),\n",
-    "    predict_times=minimal_predict_times,\n",
-    "    control_policy=LinearPolicy(K=0.5 * jnp.eye(control_dim_2d)),\n",
-    "    filter_config=PFConfig(n_particles=500),\n",
-    ")\n",
-    "assert jnp.all(jnp.isfinite(minimal_result.states))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "17de102b",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "11e0c759",
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {