Adaptative high-gain extended Kalman filter and applications

tel-00559107, version 1 - 24 Jan 2011
Chapter 1
Introduction
Juggling. Balls fly in thin air, tracing parabolas. The juggler sees, and reacts. Eyes move,
muscles follow, and the improbable act of using only two hands to keep three, four, five or
even more balls in the air continues, non-stop.
It goes without saying that the juggler has both eyes open. Why, though? With one eye
closed, the juggling becomes harder, as depth perception becomes di?cult and field of view
more limited. Juggling with one eye closed can be done, but only at the cost of training and
perseverance.
What about juggling blindfolded? Only the best jugglers can do this by inferring the
position of each ball from their hands and the accuracy of their throws. This is because they
know what the parabola should look like.
When we rely on partial measurements to reconstruct the state of a physical process,
we are like blindfolded jugglers. We only have limited information to tell us the di?erence
between what we think the state is and what it actually is. In process control, the tool
dedicated to the state reconstruction task is known as an observer.
An observer is a mathematical algorithm that estimates the state of a system. What
makes the observer special is that it does not guess. It infers, based on a prediction of what
it expects to measure and a correction driven by the difference between the predicated and
the measured.
The concept of observer is introduced in this chapter with only little mathematical formalism.
We provide an idea of the ma jor issues of the field and put forward the motivations
underlying the present work.
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