What does a controller designed in a twin with the wrong actuator gain cost in the real world?

research/control-twin

A controller designed in a twin with the wrong actuator gain: exact real LQR cost, an instability band the twin does not warn about, closed-loop non-identifiability without dither, and a dithered retune with matched regret law.

10 tests

What it found

For a scalar LQR controller (plant x′=ax+bu+w) the real cost under the twin’s gain K is exactly (q+rK²)W/(1−(a−bK)²). With a=0.9, a twin that believes the actuator is half as strong claims 1.245 but costs 1.508 (+40%); at 0.2× the real loop is unstable while the twin claims a finite cost. Unlike an estimator, a controller has an instability cliff (m < a/(a+1) as r→0), which is a band when control is penalised, and a too-strong twin is the safer error (+20% vs +40% at a factor of 2). Negative result: running the twin’s controller on the real system identifies only the closed-loop pole, not a and b; with dither the least-squares covariance is closed-form and the retune regret matches a delta-method law (∝1/n), while dither costs performance and its optimum shrinks with the data budget. Stylised: scalar linear-Gaussian, stationary, known a.

A figure from its own output

Figure produced by research/control-twin: twin_ratio — control-twin/experiments/twin_ratio.svg, written by the project's own experiment code.

Paper, code and results

More in Digital twins & sim-to-real

How long does a simulator without actuator limits say an unstable plant stays in control?A limit-free twin of an unstable plant with a saturating actuator overstates mean time to loss of control by 6,295× at noise sd 1 (1.5×10⁶ vs 245 steps), an exponential-in-1/s² gap (slope ≈3.7 real vs ≈12.7–13.2 twin), though both rank the deadbeat gain best.
What does a Kalman filter tuned in an ideal-sensor twin cost on a quantizing real sensor?A Kalman filter tuned in an ideal-sensor twin, run on a quantizing sensor: twin gain costs +11% (R=1, D=4) to +64% (R=0.01), Sheppard R+D²/12 retune is within 1% of best, but its MSE claim under-predicts by up to 43% once the step exceeds the state's scale.
How should a simulation budget be split across twin fidelities?Splitting a simulation budget across twin fidelities (multilevel Monte Carlo): smooth quantity saves 3.6×–897× (rates α=1, β=2), a failure probability only β=1 so multilevel loses at loose targets (0.4×) and reaches 7.7× at 1e-4; equal samples per level cost 156×/3.9× the optimum.
How many real steps does a twin-pretrained policy save, and which twin errors does fine-tuning inherit?Fine-tuning a twin-pretrained policy on the real plant: exact SGD risk, a twin start saves 64–67% of real steps at 0.6× the cold error but is negative transfer beyond 1×, and twin error decays only as b²/(4eηk) (flat directions inherited: 13 vs 1,541 steps at equal initial loss).
How far ahead should a controller planned in a twin with the wrong plant pole look?How far ahead a controller planned in a wrong-pole twin should look: exact real cost per horizon is non-monotone when the twin overstates the pole (1.81 at H=2 vs 3.97 at H=60, optimum 1.48), the twin's own claim ranks horizons backwards, exact two-step stability edge, and a Riccati terminal cost removes the effect.
How should cheap biased twin samples be weighted against scarce real ones?Mixing cheap biased twin samples with scarce real ones: exact optimal weight, twin worth capped at σ²/δ² real samples, equal pooling helps iff δ²<a+b, and estimating the bias from data is costly (plug-in worse than real-only for large bias).

All 164 Digital twins & sim-to-real projects →

Other research topics

Proper scoring & elicitation28 Effort & peer prediction9 Verification games & slashing19 Detection & tolerances14 Markets as routers13 Prediction-market design9 Paying contributors8 Decentralised training systems23 Digital twins & sim-to-real164 LLM chip design loops40 Robot manufacturing loops53 Ambient AI assistant46 Self-replicating manufacturing34 Simulation-first design64 Engineered clothing45 Task-specific AI accelerators40 Algorithmic chip-design loops42 Open-source purpose-built robots44 The software-engineering loop43 Adversarial human imitation41 Open-source residential construction41 Autonomous multi-angle capture34 Sensing, imaging and 3D31 Energy supply and dense energy storage39 Robot societies among people31 Agentic co-design of low-cost robots27 Laundry-hanging robots25 Machine learning on qualitative data23 Robots on the building site27 Civilizations & group psychology1 History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.