Track radiator lag across relay changes

The lag proxy was reset to the new relay command at every relay change
and after any skipped interval, so it read 1.0 straight after ON and 0.0
straight after OFF. This disabled the lag model around every boiler
cycle: on a synthetic lagged plant cycled by a hysteresis thermostat the
learner's heat gain came out 34% low (0.079 vs 0.12) and the loss term
43% low, and the optimizer started post-transition plans from the wrong
lag.

Track the lag at every poll with a valid relay state, independently of
room sensors. Integrate a single change between polls at its
last_changed time. For ambiguous cases (round trip between polls, relay
outage, restart, clock jump) restart from time-in-state with an explicit
error half-width, and learn only once it is at most 0.1 (about 32 min
after an HA restart). The same synthetic test now learns 0.1195/0.00389
(true 0.12/0.004).

Expose heat_lag, heat_lag_uncertainty and sample_result on Status so
users can see why a poll was or was not learned. The HA test fixture
relay now has an hour-old timestamp; a new test covers a freshly
written relay state.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

custom_components/heating_mpc/coordinator.py

@@ -19,7 +19,10 @@ from .const import (
     CONF_BAND, DEFAULTS,
 )
 from .data_quality import freshness
-from .physics import Learner, optimize
+from .physics import (
+    LAG_LEARN_MAX_UNCERTAINTY, LAG_TAU_SECONDS, Learner, advance_lag,
+    lag_from_time_in_state, optimize,
+)
 from .weather_sources import choose_weather_sources, sources_for, normalize
 
 _LOGGER = logging.getLogger(__name__)
@@ -36,7 +39,9 @@ class HeatingMPCCoordinator(DataUpdateCoordinator[dict[str, Any]]):
         self.learners: dict[str, Learner] = {room: Learner() for room in self.rooms}
         self._store = Store(hass, 1, f"{DOMAIN}.{entry.entry_id}")
         self._previous: dict[str, Any] | None = None
-        self._heat_lag: float | None = None
+        # Radiator-lag proxy at the last poll with a valid relay state. Tracked
+        # independently of room sensors so lag survives room outages and transitions.
+        self._lag: dict[str, Any] | None = None
         self._on_samples = 0
         self._off_samples = 0
 
@@ -73,6 +78,34 @@ class HeatingMPCCoordinator(DataUpdateCoordinator[dict[str, Any]]):
         return freshness(getattr(state, "last_reported", getattr(state, "last_updated", None)),
                          now, limit * 60)
 
+    def _track_lag(self, now: datetime, heater_on: bool, last_changed: datetime) -> bool:
+        """Advance the lag proxy to `now`; return True if the relay held one state throughout.
+
+        A single relay change since the last poll is integrated at its timestamp.
+        Anything ambiguous (several changes, an outage, clock jumps) restarts the
+        estimate from the time spent in the current state, with an explicit error bound.
+        """
+        tracker = self._lag
+        steady = False
+        lag = uncertainty = None
+        if tracker is not None:
+            dt = (now - tracker["time"]).total_seconds()
+            if dt > 0 and heater_on == tracker["heater_on"] and last_changed <= tracker["time"]:
+                lag = advance_lag(tracker["lag"], heater_on, dt)
+                steady = True
+            elif dt > 0 and heater_on != tracker["heater_on"] and tracker["time"] < last_changed <= now:
+                before = (last_changed - tracker["time"]).total_seconds()
+                lag = advance_lag(tracker["lag"], tracker["heater_on"], before)
+                lag = advance_lag(lag, heater_on, (now - last_changed).total_seconds())
+            if lag is not None:
+                # The lag update is a contraction, so an initial error decays the same way.
+                uncertainty = tracker["uncertainty"] * exp(-dt / LAG_TAU_SECONDS)
+        if lag is None:
+            lag, uncertainty = lag_from_time_in_state(
+                heater_on, (now - last_changed).total_seconds())
+        self._lag = {"time": now, "heater_on": heater_on, "lag": lag, "uncertainty": uncertainty}
+        return steady
+
     async def _async_update_data(self) -> dict[str, Any]:
         now = datetime.now(timezone.utc)
         heater = self.hass.states.get(self.config[CONF_HEATER])
@@ -131,34 +164,44 @@ class HeatingMPCCoordinator(DataUpdateCoordinator[dict[str, Any]]):
             "weather_comparison": {k: v for k, v in weather_comparisons.items() if v},
             "weather_model_inputs": ["temperature"],
         }
-        if heater is None or heater.state not in ("on", "off") or climate is None:
+        heater_valid = heater is not None and heater.state in ("on", "off")
+        heater_on = heater_valid and heater.state == "on"
+        steady = False
+        if heater_valid:
+            steady = self._track_lag(now, heater_on, heater.last_changed)
+            status["heat_lag"] = round(self._lag["lag"], 3)
+            status["heat_lag_uncertainty"] = round(self._lag["uncertainty"], 3)
+        else:
+            self._lag = None
+        if (not heater_valid or climate is None or outside is None or
+                any(temp is None for temp in temps.values())):
             self._previous = None
-            self._heat_lag = None
-            return status
-        if outside is None or any(temp is None for temp in temps.values()):
-            self._previous = None
-            self._heat_lag = None
             return status
 
         # No casting surprises: all rooms are valid here.
         vals: dict[str, float] = {room: float(temps[room]) for room in self.rooms}
-        heater_on = heater.state == "on"
+        if self._previous is None:
-        if self._heat_lag is None:
+            status["sample_result"] = "first_sample"
-            self._heat_lag = float(heater_on)
+        else:
-        if self._previous is not None:
             dt = (now - self._previous["time"]).total_seconds()
-            # Do not fit one transition across a provider/fallback switch.
+            # Do not fit across a relay change, a provider/fallback switch or an
-            if (270 <= dt <= 330 and
+            # uncertain lag estimate (restart, relay outage, several changes).
-                    heater.last_changed <= self._previous["time"] and
+            if not 270 <= dt <= 330:
-                    heater_on == self._previous["heater_on"] and
+                status["sample_result"] = "interval_out_of_range"
-                    self._previous["outside_source"] == active_sources["temperature"]):
+            elif not steady or heater_on != self._previous["heater_on"]:
-                next_lag = self._heat_lag + (1 - exp(-dt / 1200)) * (float(self._previous["heater_on"]) - self._heat_lag)
+                status["sample_result"] = "relay_changed"
-                for room in self.rooms:
+            elif self._previous["outside_source"] != active_sources["temperature"]:
+                status["sample_result"] = "outside_source_changed"
+            elif self._lag["uncertainty"] > LAG_LEARN_MAX_UNCERTAINTY:
+                status["sample_result"] = "lag_uncertain"
+            else:
+                accepted = [
                     self.learners[room].learn(
                         self._previous["temps"][room], vals[room],
-                        self._previous["outside"], next_lag, dt, self._previous["heater_on"]
+                        self._previous["outside"], self._lag["lag"], dt, heater_on)
-                    )
+                    for room in self.rooms
-                self._heat_lag = next_lag
+                ]
+                status["sample_result"] = "learned" if all(accepted) else "partly_rejected"
                 self._update_counts()
                 # Persist at each sample so restart does not erase hours of training.
                 await self._store.async_save({
@@ -168,9 +211,6 @@ class HeatingMPCCoordinator(DataUpdateCoordinator[dict[str, Any]]):
                     "heater_entity": self.config[CONF_HEATER],
                     "outside_source": active_sources["temperature"],
                 })
-            else:
-                # Model lag state becomes uncertain after long gaps.
-                self._heat_lag = float(heater_on)
 
         self._previous = {
             "time": now, "temps": vals, "outside": outside, "heater_on": heater_on,
@@ -224,7 +264,7 @@ class HeatingMPCCoordinator(DataUpdateCoordinator[dict[str, Any]]):
             # never block Home Assistant's event loop with CPU work.
             job = partial(
                 optimize,
-                vals, outside, self._heat_lag, target, weights, self.learners,
+                vals, outside, self._lag["lag"], target, weights, self.learners,
                 heater_on, (now - heater.last_changed).total_seconds(),
                 horizon_minutes=int(self.config[CONF_HORIZON]),
                 minimum_on_minutes=int(self.config[CONF_MIN_ON]),

custom_components/heating_mpc/physics.py

@@ -11,7 +11,11 @@ from math import exp, isfinite
 from typing import Any
 
 STEP_MINUTES = 5
-HEAT_LAG = 1.0 - exp(-STEP_MINUTES / 20.0)
+# First-order radiator lag between the relay command and the heat reaching rooms.
+LAG_TAU_SECONDS = 1200.0
+HEAT_LAG = 1.0 - exp(-STEP_MINUTES * 60 / LAG_TAU_SECONDS)
+# Learn only when the lag proxy is known within this half-width.
+LAG_LEARN_MAX_UNCERTAINTY = 0.1
 # Prior covariance; also the upper bound that stops RLS windup (see _bound_covariance).
 PRIOR_P = ((0.0005, 0.0, 0.0), (0.0, 0.8, 0.0), (0.0, 0.0, 0.08))
 
@@ -20,6 +24,22 @@ def bound(value: float, lo: float, hi: float) -> float:
     return max(lo, min(hi, value))
 
 
+def advance_lag(lag: float, command: bool, seconds: float) -> float:
+    """Move the lag proxy towards the relay command over `seconds`."""
+    return lag + (1.0 - exp(-seconds / LAG_TAU_SECONDS)) * (float(command) - lag)
+
+
+def lag_from_time_in_state(command: bool, seconds_in_state: float) -> tuple[float, float]:
+    """Estimate the lag when only the time since the last relay change is known.
+
+    Starting from any unknown lag in [0, 1], `seconds_in_state` of a constant command
+    leaves the lag inside an interval of width exp(-t/tau). Return its midpoint and
+    half-width, so the error bound is explicit rather than assuming a steady state.
+    """
+    width = exp(-max(0.0, seconds_in_state) / LAG_TAU_SECONDS)
+    return (1.0 - width / 2) if command else width / 2, width / 2
+
+
 def _bound_covariance(p: list[list[float]]) -> None:
     """Keep P symmetric and no less certain than the prior, in place.
 

tests/ha/conftest.py

@@ -3,6 +3,7 @@ from unittest.mock import patch
 
 import pytest
 from homeassistant.core import ServiceRegistry
+from homeassistant.util import dt as dt_util
 from pytest_homeassistant_custom_component.common import MockConfigEntry
 
 
@@ -36,5 +37,6 @@ def entry():
 def inputs(hass):
     hass.states.async_set("sensor.room", "20", {"unit_of_measurement": "°C"})
     hass.states.async_set("sensor.outside", "5", {"unit_of_measurement": "°C"})
-    hass.states.async_set("switch.boiler", "off")
+    # The relay has held its state for an hour, so the radiator-lag estimate is settled.
+    hass.states.async_set("switch.boiler", "off", timestamp=dt_util.utcnow().timestamp() - 3600)
     hass.states.async_set("climate.reference", "heat", {"temperature": 22, "preset_mode": "comfort"})

tests/ha/test_lifecycle.py

@@ -146,3 +146,17 @@ async def test_startup_missing_inputs_then_recovery(hass, entry):
     await coordinator.async_refresh()
     assert coordinator.data["status"] == "learning"
     assert coordinator.data["samples"] == 0
+
+
+async def test_freshly_written_relay_state_defers_learning(hass, entry, inputs, freezer):
+    """After an HA restart the relay's last_changed is new, so radiator lag is unknown."""
+    hass.states.async_set("switch.boiler", "on")
+    coordinator = await setup(hass, entry)
+    assert coordinator.data["heat_lag"] == 0.5
+    assert coordinator.data["heat_lag_uncertainty"] == 0.5
+    future = dt_util.utcnow() + timedelta(minutes=5, seconds=1)
+    freezer.move_to(future)
+    async_fire_time_changed(hass, future)
+    await hass.async_block_till_done()
+    assert coordinator.data["sample_result"] == "lag_uncertain"
+    assert coordinator.learners["sensor.room"].count == 0

tests/test_coordinator.py

@@ -4,6 +4,7 @@ import sys
 import types
 import unittest
 from datetime import datetime, timedelta, timezone
+from math import exp, pi, sin
 from pathlib import Path
 from unittest.mock import AsyncMock, Mock, patch
 
@@ -92,6 +93,12 @@ class BoundaryTests(unittest.IsolatedAsyncioTestCase):
         self.now += timedelta(seconds=seconds)
         return data
 
+    def switch(self, state, seconds_before_next_sample):
+        """Change the relay between polls; `self.now` is already the next poll time."""
+        heater = self.states['switch.boiler']
+        heater.state = state
+        heater.last_changed = self.now - timedelta(seconds=seconds_before_next_sample)
+
     def ready(self):
         m = self.c.learners['sensor.room']
         m.count, m.on_count, m.off_count = 200, 100, 100
@@ -310,3 +317,98 @@ class BoundaryTests(unittest.IsolatedAsyncioTestCase):
         data = await self.sample()
         self.assertEqual(data['input_quality']['weather']['temperature']['sensor.outside']['status'],
                          'invalid_value_or_unit')
+
+    async def test_lag_is_continuous_across_relay_transitions(self):
+        advance = coordinator.advance_lag
+        await self.sample()
+        lag = self.c._lag['lag']
+        self.switch('on', 150)
+        data = await self.sample()
+        lag = advance(advance(lag, False, 150), True, 150)
+        self.assertEqual(data['sample_result'], 'relay_changed')
+        self.assertAlmostEqual(self.c._lag['lag'], lag)
+        self.assertLess(lag, 0.2)  # radiators have only started warming, not 1.0
+        data = await self.sample()
+        lag = advance(lag, True, 300)
+        self.assertEqual(data['sample_result'], 'learned')
+        self.assertAlmostEqual(self.c._lag['lag'], lag)
+        self.switch('off', 100)
+        await self.sample()
+        lag = advance(advance(lag, True, 200), False, 100)
+        self.assertAlmostEqual(self.c._lag['lag'], lag)
+        self.assertGreater(lag, 0.3)  # residual radiator heat is kept, not 0.0
+
+    async def test_prediction_starts_from_tracked_lag(self):
+        self.ready()
+        self.set_state('switch.boiler', 'on')
+        await self.sample()
+        self.switch('off', 60)
+        with patch.object(coordinator, 'optimize', wraps=coordinator.optimize) as spy:
+            data = await self.sample()
+        self.assertEqual(data['status'], 'ready')
+        self.assertAlmostEqual(spy.call_args.args[2], self.c._lag['lag'])
+        self.assertGreater(spy.call_args.args[2], 0.9)
+
+    async def test_round_trip_between_polls_restarts_lag_estimate(self):
+        await self.sample()
+        self.switch('off', 60)  # off -> on -> off; only the last change is visible
+        data = await self.sample()
+        self.assertEqual(data['sample_result'], 'relay_changed')
+        self.assertEqual(data['heat_lag_uncertainty'], round(exp(-60 / 1200) / 2, 3))
+        data = await self.sample()
+        self.assertEqual(data['sample_result'], 'lag_uncertain')
+        self.assertEqual(self.c.learners['sensor.room'].count, 0)
+
+    async def test_learning_waits_until_lag_settles_after_restart(self):
+        self.states['switch.boiler'].last_changed = self.now  # HA restart resets last_changed
+        results = []
+        for _ in range(8):
+            for entity in ('sensor.room', 'sensor.outside'):
+                self.states[entity].last_reported = self.now
+            results.append((await self.sample())['sample_result'])
+        self.assertEqual(results[0], 'first_sample')
+        self.assertEqual(results[1:7], ['lag_uncertain'] * 6)
+        self.assertEqual(results[7], 'learned')
+
+    async def test_room_outage_keeps_relay_lag_tracking(self):
+        await self.sample()
+        self.switch('on', 150)
+        self.states['sensor.room'].state = 'unavailable'
+        data = await self.sample()
+        self.assertEqual(data['status'], 'waiting_for_sensors')
+        self.assertLess(data['heat_lag'], 0.2)
+
+    async def test_relay_outage_restarts_lag_estimate(self):
+        await self.sample()
+        self.states['switch.boiler'].state = 'unavailable'
+        data = await self.sample()
+        self.assertNotIn('heat_lag', data)
+        self.switch('off', 30)
+        data = await self.sample()
+        self.assertEqual(data['sample_result'], 'first_sample')
+        self.assertGreater(data['heat_lag_uncertainty'], 0.4)
+
+    async def test_heat_gain_identified_with_mid_interval_switching(self):
+        """Synthetic plant with radiator lag, cycled by a hysteresis thermostat."""
+        a, b, c = 0.004, 0.12, 0.0005
+        advance = coordinator.advance_lag
+        self.states['climate.reference'].state = 'off'  # learn only
+        temp, lag, on = 21.0, 0.0, False
+        for k in range(1500):
+            outside = 5 + 5 * sin(2 * pi * k / 288)
+            for entity, value in (('sensor.room', temp), ('sensor.outside', outside)):
+                self.states[entity].state = f'{value:.5f}'
+                self.states[entity].last_reported = self.now
+            await self.sample()
+            command = temp < 20.7 or (on and temp < 21.3)
+            if command != on:  # relay switches 120 s after this poll
+                self.switch('on' if command else 'off', 180)
+                lag = advance(advance(lag, on, 120), command, 180)
+            else:
+                lag = advance(lag, on, 300)
+            on = command
+            temp += a * (outside - temp) + b * lag + c
+        model = self.c.learners['sensor.room']
+        self.assertGreater(model.on_count, 100)
+        self.assertAlmostEqual(model.theta[1], b, delta=0.1 * b)
+        self.assertAlmostEqual(model.theta[0], a, delta=0.25 * a)

tests/test_physics.py

@@ -135,5 +135,19 @@ class ModelTests(unittest.TestCase):
         self.assertEqual(restored.p[0][0], m.PRIOR_P[0][0])
         self.assertEqual(restored.p[0][1], restored.p[1][0])
 
+    def test_lag_helpers(self):
+        self.assertAlmostEqual(m.advance_lag(0, True, 300), m.HEAT_LAG)
+        self.assertAlmostEqual(m.advance_lag(1, False, 1e9), 0)
+        self.assertEqual(m.lag_from_time_in_state(True, 0), (0.5, 0.5))
+        lag, half_width = m.lag_from_time_in_state(False, 3600)
+        self.assertAlmostEqual(lag, half_width)
+        self.assertLess(half_width, 0.03)
+        # Any starting lag in [0, 1] ends inside the stated interval.
+        for start in (0.0, 0.3, 1.0):
+            for command in (False, True):
+                lag, half_width = m.lag_from_time_in_state(command, 900)
+                self.assertLessEqual(abs(m.advance_lag(start, command, 900) - lag), half_width + 1e-12)
+
+
 if __name__ == '__main__':
     unittest.main()