Publication
Published in the International Journal of Topology (MDPI, ISSN 2813-9542), 3(2), 9 — open access under CC BY. Received 20 December 2025; revised 9 February 2026; accepted 3 April 2026; published 12 May 2026. Academic editors: Michel Planat and Edward A. Rietman.
- DOI: 10.3390/ijt3020009
- Journal page: mdpi.com/2813-9542/3/2/9
At a glance
Most perception-for-control pipelines treat representation learning and controller synthesis as separate problems. The central claim here is that the topology of the representation space is itself a control-theoretic object: recognising this lets us state delay-robustness guarantees in terms of cohomological invariants of the learned ontology, and lets us build controllers — the ORTSF operators — that exploit precisely that structure.
Contributions
- ONN architecture. A neural model whose latent state inherits the type structure of a target ontology rather than being a flat vector. Forman–Ricci curvature, persistent homology, and semantic tensor structures are folded into a unified loss so that relational integrity is preserved as scenes evolve (Theorems 1, 2, 5, 7).
- ORTSF operators. A composition of predictive and compensating operators that transform the ONN's reasoning trace into delay-robust control commands, preserving closed-loop phase margin (Theorems 3, 4, 6).
- Unified seven-theorem framework. Convergence, uniqueness, tracking, delay stability, constraint handling, and contextual adaptation guarantees, tied together by Theorem 8.
- Empirical validation. Theoretical analysis plus extensive simulations confirming that ORTSF maintains designed phase margins and outperforms classical delay-compensation baselines on topologically-conditioned tasks.
Keywords
ontology neural network · semantic fabric · topological reasoning · delay-robust control · cognitive robotics
Where this sits in the broader programme
This paper is the first formal statement of the ONN + ORTSF framework. It sits downstream of the RelationWorld mathematical foundations (see the notes) and upstream of the cognitive-robotics work on collaborative manipulation. Related recent manuscripts include Constructive Lyapunov Functions via Topology-Preserving Neural Networks and Advanced Topology-Preserving Neural Networks, both listed in the papers index.