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 State Feedback) 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, and their composition obeys stability bounds stated in the language of the learned ontology's cohomology rather than raw state norms.
What has been shown
- A constructive resolution of the Massera–Kurzweil problem. For systems governed by an ONN, an explicit class- Lyapunov function is available — no trajectory integrals, no existence-only proofs.
- Explicit delay bounds. For 3M-node semantic networks, the framework admits delays up to while maintaining exponential convergence.
- Four domains of applicability: non-smooth dynamics via Fejér-monotone topology surgery, global stability via persistent homology (Betti-number preservation), delay-differential systems via ORTSF, and Input-to-State Stability for bounded disturbances.
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 — from physical event to ready observation.
- Perception delay — from observation to latent state update.
- Decision delay — from latent state to control signal.
- Actuation delay — 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 — the empirical realisation of the above bounds.
Related
- Ontology Neural Networks — the upstream layer whose latent state the controllers consume.
- Robotics — physical platforms used to ground these results in hardware.