Z.t is influenced by S.[<t] and R.[<t], the curren state of Z is the result of the time series of S up to that point and the timeseries of R up to that point.
Think of each arrow as taking 1 time quantum. Even if you assume R itself takes 0 prossessing time, R can only affect Z after S already had it's affect.
So S.t affects Z.t+1 and is observed by R at t+1, and the regulatory signal from the resulting output of R will only affect at Z.t+2 at the same time that S.t+1 is already affecting it.
If R has no implicit or explicit model of the S-Z relation, meaning it can not sufficiently predict dZ from dS, it can not modulate dR, its own compensations, to avoid over or undercompensating.
In practice you see this in self reinforcing feedbackloops in naive regulators. An initial small perturbation gets overcompensated so the result is a slightly larger perturbation that gets overcompensated until the system is completely oscilating out of control.
amatic•7mo ago
> The archetypal example for this is something like a thermostat. The variable S represents random external temperature fluctuations. The regulator R is the thermostat, which measures these fluctuations and takes an action (such as putting on heating or air conditioning) based on the information it takes in. The outcome Z is the resulting temperature of the room, which depends both on the action taken by the regulator, and the external temperature.
The problem here is that the regulator R does not measure external temperature. It just measures the controlled variable - the temperature Z, so the causal arrow should go from Z to R too, and the arrow from S to R does not exist.
analog31•7mo ago
masfuerte•7mo ago
Domestic thermostats typically don't but some heating control systems do.