"Time for control"

[From Matti Kolu (2014.04.16.1900 CET)]


"In engineering and mathematics, t is the quintessential independent
variable: an immutable quantity in terms of which all other variables
depend. Most control systems do require a clock, but clocks have been
engineered with such low drift rates that for all practical purposes,
imperfections in chronometry have been largely ignored.

Biological systems do not have it so easy. Biological clocks were not
“engineered�? on top of a physical phenomenon like the oscillation of a
quartz crystal. Rather, biological wetware must keep time over many
scales using physiological, neural, and biochemical mechanisms.
Biological clocks are typically described as nonlinear dynamical
systems exhibiting limit cycle behavior where the phase of the system
advances monotonically with the passage of time. For example,
circadian rhythms and other longer-term processes highlight the
importance of external cues in the timekeeping process. Circadian and
circannual rhythms, for example, are regulated by changes in
daylength, temperature, and other environmental cues.

So, while uncertainty in time is justifiably neglected in the design
and analysis of most engineering control systems, perfect timekeeping
is a poor assumption for the modeling and analysis of biological
control systems. Indeed, timekeeping during simple human motor control
tasks involves errors of around 10% of the movement cycle duration.
Despite this extremely high level of temporal imprecision, the
overwhelming majority of computational models of the human motor
control makes the implicit assumptions that time is known. Who knows
what happens to any of these analyses when our assumption about
perfect timekeeping is relaxed?"

S. M. LaValle and M. B. Egerstedt, “On time: Clocks, chronometers, and
open-loop control,�? in Proc. IEEE Int. Conf. on Decision Control,
2007, pp. 1916�1922.


S. G. Carver, E. S. Fortune, and N. J. Cowan, “State-estimation and
cooperative control with uncertain time,�? in Proc. Amer. Control
Conf., 2013, in press.

A. Lamperski and N. J. Cowan, “Time-changed linear quadratic
regulators,�? in Proc. Euro. Control Conf., 2013, in press.