Delay-robust control

Perception and control meet in the presence of delay. Once you allow that sensing, compute, and network communication each introduce non-negligible lag, the classical separation between "figure out what the world is" and "decide what to do about it" becomes untenable — the two problems interact through the delay.

This track collects the stability analyses and predicate-binding gates that remain after audit. No verified result currently links their closed-loop stability to the topology of the upstream representation.

The ORTSF framework#

ORTSF (Ontological Real-Time Semantic Fabric) is a family of predicate-binding operators whose job is to synthesise a control signal from an ONN latent state while preserving the meaning encoded in that state. The operators carry explicit delay budgets.

What has been shown#

• A scoped sufficient condition. For the scalar recurrence $e[t+1] = \rho e[t] - K_c e[t-d]$, the condition $\rho + |K_c| < 1$ is sufficient for Schur stability for every integer delay $d \geq 1$. This does not establish coupled multimode or deployed-controller stability; the $B$-operator bound, mapping $K_c$ to physical PD gains, and full-system lift remain open.
• What was withdrawn. The "constructive resolution of the Massera–Kurzweil problem", the specific τ_max = 177 μs / 3M-node bound, and the cohomological-Lyapunov reading are not reproducible from the current research source and are retired — see the ONN research status.

The budget-first view#

Before reaching for a full stability analysis it pays to decompose the end-to-end delay of a perception-control loop into a budget: a small set of line items each tied to a term in the analysis and each independently measurable. A first pass:

• Sensing delay $\tau_s$ — from physical event to ready observation.
• Perception delay $\tau_p$ — from observation to latent state update.
• Decision delay $\tau_d$ — from latent state to control signal.
• Actuation delay $\tau_a$ — from signal to effect on plant.

With this structure the stability margin can be stated per-term, which is more actionable than a scalar bound.

Papers on this track#

• Ontology Neural Network and ORTSF: A Framework for Topological Reasoning and Delay-Robust Control — the published paper of record for the original framing; later audit narrows its control claim as described above.
• Constructive Lyapunov Functions via Topology-Preserving Neural Networks
• Advanced Topology-Preserving Neural Networks — a 2025 draft that claimed the empirical realisation of these bounds; superseded by the audit (see its status banner).

Related#

• Ontology Neural Networks archive — the historical representational layer whose latent state the controllers were intended to consume.
• Unified Latent Representation — the active programme that now tests representation and role claims against typed baselines.
• Robotics — physical platforms used to ground these results in hardware.