A Method for Handling Uncertainty in Evolutionary Optimization with an
Application to Feedback Control of Combustion

       Nikolaus Hansen, Andre S.P. Niederberger, 
        Lino Guzzella, and Petros Koumoutsakos

We present a novel method for handling uncertainty in evolutionary
optimization.  The method entails quantification and treatment of
uncertainty and relies on the rank based selection operator of
evolutionary algorithms.  The proposed uncertainty handling is
implemented in the context of the Covariance Matrix Adaptation
Evolution Strategy (CMA-ES) and verified on test functions. The
present method is independent of the uncertainty distribution,
prevents premature convergence of the evolution strategy and is well
suited for online optimization as it requires only a small number of
additional function evaluations.  The algorithm is applied in an
experimental set-up to the online optimization of feedback controllers
of thermoacoustic instabilities of gas turbine combustors. In order to
mitigate these instabilities, gain-delay or model-based
$\mathcal{H}_\infty$ controllers sense the pressure and command
secondary fuel injectors.  The parameters of these controllers are
usually specified via a trial and error procedure.  We demonstrate
that their online optimization with the proposed methodology enhances,
in an automated fashion, the online performance of the controllers,
even under highly unsteady operating conditions, and it also
compensates for uncertainties in the model-building and design
process.