νgap barycenter synthesis

[baggepinnen]

For an uncertain system Gu represented by multiple models (e.g., Particles), one could design a controller that is guaranteed to be stabilizing for all plants in Gu by first finding a nominal plant which is the νgap barycenter of Gu (central plant in the νgap metric), and then constrain the control design to have NCF margin greater than the largest νgap between the nominal plant and any realization in Gu.

To compute the νgap barycenter, see https://research.abo.fi/ws/portalfiles/portal/25079057/HaggblomFinal.pdf

A simple first approach would be to use a user-selected nominal model, or the coefficient mean. For a small number of models, one can compute all pairwise νgaps and select the model that has the smallest maximum. For sampled models, this might do well, but it might do poorly for a set of "corner models".

The νgap computation is somewhat expensive, but not prohibitive.

julia> P1 = ssrand(5,5,20);

julia> P2 = ssrand(5,5,20);

julia> @btime nugap($P1, $P2)
  3.417 ms (2893 allocations: 4.09 MiB)