[From Matti Kolu (2014.04.16.1900 CET)]

http://limbs.lcsr.jhu.edu/2013/06/08/449/

"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.

http://msl.cs.uiuc.edu/~lavalle/papers/LavEge07.pdf

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.

http://limbs.lcsr.jhu.edu/wp-content/uploads/2013/06/2013ACC_1675_FI.pdf

A. Lamperski and N. J. Cowan, “Time-changed linear quadratic

regulators,�? in Proc. Euro. Control Conf., 2013, in press.

http://limbs.lcsr.jhu.edu/wp-content/uploads/2013/06/lamperskitimechanged2013-njc.pdf

Matti