Probabilistic and Deterministic Algorithms for Information and Dynamic Systems.

Abstract

The central goal of control engineering is to assure the robust stability and performance for systems in the presence of uncertainties. This thesis deals with these fundamental issues in three different frameworks. First, the robustness of uncertain systems are discussed in the structured singular value mu framework. Parallel algorithms are developed which greatly facilitates robustness analysis. Second, the robust control problems are tackled in the Kharitonov framework. Efficient Algorithms have been developed for computing the robust D -stability margin for arbitrary root domain D . This allows for a more sophisticated analysis of system robustness. Finally, aimed at breaking through the barrier of NP hardness and reducing conservativeness, the robust control problems are considered in the probabilistic framework. Minimum computational effort for robust analysis with a certain degree of reliability is investigated and related sample sizes are derived. An interesting link between classic order statistics theory and robust control is established. Moreover, the classic order statistics distribution theory is generalized to accommodate discontinuous populations.