Pareto Suboptimal Robust Controllers in Multi-Objective Generalized H2 Problem

摘要

A novel multi-objective robust control problem is studied for systems with structured norm-bounded uncertainty and robust generalized H2norms as criteria. Necessary conditions for Pareto optimality are formulated. Pareto optimal solutions turn out to be among optimal solutions for multiobjective costs in the form of Germeyer convolution. Pareto suboptimal controllers are defined as the optimal solutions for the upper bounds of the multi-objective costs and characterized in terms of LMIs. The upper and lower bounds of the multi-objective cost are used to compute a suboptimality measure which allows to estimate a “difference” between Pareto suboptimal and unavailable Pareto optimal controllers. Two-criteria robust control problem for a mathematical model of the rotor rotating in active magnetic bearings is considered as an application of this theory.