DIAMANT problem

Balanced infinite designs

Construct an infinite random sequence with the following properties:

2a. and 2b. are imposed to have relatively equidistributed sequences of symbols; 2c. will further be explained below.

Context of the problem

The Technische Universiteit Eindhoven, Eurandom and Philips Research (all three in Eindhoven, the Netherlands) are collaborating within a joint-venture on Battery Management. This research is both theoretical and experimental.

Imagine that you charge a battery by a sequence of pulses that are periodically applied, namely at times ..., t-1, t, t+1, ... and that you have K sorts of pulses; furthermore, during the experiment, you record a few relevant parameters describing the battery state.

The experiment must permit us to evaluate the effect of each pulse sort (see 2a), the effect of each pulse sort transition (see 2b) and battery state drifts. These drifts have large time constants, T >> 1. To properly estimate the drifts, you need that SL be little correlated to time t; this leads to above 2c. Other sorts of correlations can clearly be considered.

Questions

  1. Did you ever see such a problem before? Do you know of any field where this problem would occur? (people names, references, ...).
  2. How to construct such sequences?
  3. What are the interesting properties of such a sequence?

Example

Using computer brute force, we constructed a sequence that is presently used for the experiments. It is a variation on the above presented theme.

Correspondent

William Rey (w_rey@tvcablenet.be)






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