Context
From U16 to U20 of the exchange “Analyze nucleation concepts” (2026-10-31)
the assistant’s constructions rested on control-theoretic tools: barrier
certificates for viable boxes, Nagumo-type invariance, small-gain
conditions, an allocation controller with reserved minima, and a safe
adaptive controller’s limit. The owner said at U17, “I bet control theory
has a bunch of tools that would be useful to us”. Two works filed from the
exchange, Kolathaya and Ames on input-to-state safety and Saligrama on when
safe controllers can adapt, had no topic that named their subject, and
were filed under mathematics.
The record already held control theory without a word for it: Aubin’s
viability theory (LIT-738, LIT-714, THEORY-134) and the contraction
analysis of singularly perturbed systems (LIT-1292, THEORY-771,
THEORY-773), all under mathematics and complex-systems. The filing
of 2026-10-31 asked the owner whether control theory needed a topic, and
the owner said yes. ADR-062 records the owner’s word that the vocabulary
may be expanded where merited.
Decision
Add one topic, control-theory (Control theory): the analysis and
design of feedback, meaning how a system’s inputs can be chosen, or are
chosen by part of the system, to keep it stable, safe or viable, or to
steer it. It covers:
- stability and Lyapunov functions;
- invariance and viability, and barrier certificates;
- input-to-state stability and small-gain conditions;
- contraction analysis;
- adaptive, dual and safe control;
- controller synthesis under constraints.
How it is applied:
- First on the two works registered from the exchange, Kolathaya and Ames, and Saligrama, where it is the subject.
- Beside the existing tags on the viability and contraction entries named above, whose subject it is. Nothing is removed and primaries are unchanged. Each takes a version bump.
- Not added to dynamical-systems work without a control input, such as
bifurcation and pattern-formation readings, or to cybernetics as a
philosophy of organization. Those stay with
complex-systems.
Alternatives
- Leave the works under
mathematicsandcomplex-systems. Both are true, but neither says what these works are for. The constructions the exchange built would go on borrowing tools with nowhere to find them. - A broader
systems-theory. It would absorb cybernetics, general systems theory and dynamical systems, whichcomplex-systemsalready covers, and it would not name the feedback design that is the point.