Solution of the Benchmark Control Problem by Scenario Optimization

This article introduces a scenario optimization framework for reliability-based design given measurements of the uncertain parameters. In contrast to traditional methods, scenario optimization makes direct use of the available data thereby eliminating the need for assuming a distribution class and estimating its hyper-parameters. Scenario theory provides formal bounds on the probabilistic performance of a design decision and certifies the system ability to comply with various requirements for future/unseen observations. This probabilistic certificate of correctness is non-asymptotic and distribution-free. Furthermore, chance-constrained optimization techniques are used to detect and eliminate the effects of outliers in the resulting optimal design. The proposed framework is exemplified on a benchmark robust control challenge problem having conflicting design objectives.