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, the gates that implement predicate binding under delay, and the experimental evidence linking them to the topology of the upstream perceptual 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 standard, verified delay margin. For a linearized plant with pole $p$, the closed loop tolerates delay up to $\Delta t_{\max} = \varphi_{\mathrm{PM}}/\omega_c$, with a sufficient small-gain condition ($\rho_{\mathrm{ONN}}\cdot\gamma_{\mathrm{ortsf}} < 1$) for arbitrary delay. This is textbook control, honestly labelled as systems completion rather than novelty.
• What was withdrawn.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 anchor paper, accepted at Int. J. Topol. in April 2026.
• 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 — the upstream layer whose latent state the controllers consume.
• Robotics — physical platforms used to ground these results in hardware.