Probabilistically-robust performance optimization for controlled linear stochastic systems

This study discusses a robust controller synthesis methodology for linear time invariant systems characterized by probabilistic parameter uncertainty. The optimization of the robust performance is considered. The extension of pre-existing, synthesis approaches, such as multi-objective H₂ design, to account for probabilistic uncertainty is investigated. A design based on the concept of the reliability of the system response output is also considered. Analysis and synthesis methodologies based on stochastic simulation techniques are discussed. The design approach is applied in a structural control example. The results illustrate the differences between the various probabilistic performance objectives and the importance of adopting a probabilistic characterization for model uncertainty when compared to nominal design or to the design using a worst-case scenario approach.