Perceptual Control Theory · Interactive Demonstration

Shared Substrate Contention

Four models, one experiment: what happens when several control systems compete for a finite physical substrate?

LIVE SIMULATION
Structural claim: Classical PCT with p = M·q + d and fixed M > 0 cannot produce differential gain collapse from substrate exhaustion. ATENFEL makes the environmental state explicit: pi = Fi(q1…qn, x), where x = [C, ρ, τ]. The point is structural, not polemical: if the collapse mechanism is added to a PCT model, the resulting model is no longer the original fixed-M perceptual function.
Experiment controls
All controllers share Cmax; each has its own reference and integrator.
Ready-made scenarios
Click to load parameters and the theoretical interpretation.
Default: Flash Crash-style contention. The reference exceeds M·C, so persistent error can drive integrator runaway after substrate collapse.
Runaway condition rA > M·CTRUE — RUNAWAY POSSIBLE
Current regimeINITIALISING
Model 1

Classical PCT — Marken

Fixed M
p = M · q + d
∂p/∂q = M > 0
The perceptual function has a constant environmental gain. Shared substrate capacity is not represented as a state, so differential collapse is structurally absent.
pA0.00
Model 2

ATENFEL — substrate state

Physical
pi = Fi(q1…qn, x)
x = [C, ρ, τ]
The shared substrate couples controllers. As total demand approaches capacity, local effective gain can collapse toward zero for an individual controller.
∂pA/∂qA1.000
Model 3

Marken + effective gain

Augmented
p = M · f(ρ) · q + d
f(ρ) = 1 − ρ
Collapse can be represented, but only after explicitly making environmental loading part of the effective gain. That state-dependent M is an augmentation, not the original fixed-M form.
M·f(ρ)1.000
Model 4

Marken + variable d

Reformulated
p = M · q + d(q,ρ)
d is state-dependent
Collapse can be rewritten as a variable disturbance term, but d is no longer an independent disturbance. It is carrying the missing nonlinear environmental mechanism.
dA0.00

Perception and reference

rA vs pA

Outputs and substrate load

qA · qB…n · ρ

Local effective gain

∂pA/∂qA

Prediction error over recent history

last 5 seconds
Real-time diagnostic metrics
Physical model / Controller A
Error eA
0.00
rA − pA
Effective gain
1.000
∂pA/∂qA
Saturation
0.0%
ρ = T/C
Control cost
0.0
∫ Σq² dt
Runaway time
—
persistent error + growth
Deviation from ATENFEL
—
MSE vs physical model
Total demand
0.0
Σ q delayed
qA
0.0
integrator state
pA
0.0
ATENFEL perception
Cmax
5
shared capacity
Agents
3
controllers
Time
0.0s
simulation clock
Reading the experiment: a collapse of Model 2's local gain is the central event. It does not automatically imply runaway. Runaway requires rA > M·C; otherwise the system can settle at a new equilibrium with reduced perception.