A novel multi-objective robust control problem is studied for systems with norm-bounded structured uncertainty and robust generalised norms as criteria. Necessary conditions for Pareto optimality are formulated from which it follows that Pareto optimal solutions are to be among optimal solutions for scalar multi-objective costs in the form of Germeyer convolution. The upper bounds of the multi-objective costs are used to compute Pareto suboptimal controllers in terms of linear matrix inequalities, while the lower bounds 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.

中文翻译：

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多目标鲁棒广义H 2 控制

针对以范数有界结构不确定性和鲁棒广义范数为准则的系统，研究了一个新的多目标鲁棒控制问题。帕累托最优的必要条件被公式化，由此得出帕累托最优解是 Germeyer 卷积形式的标量多目标成本的最优解之一。多目标成本的上限用于根据线性矩阵不等式计算帕累托次优控制器，而下限用于估计帕累托次优和不可用的帕累托最优控制器之间的“差异”。主动磁轴承中转子旋转的数学模型的双准则鲁棒控制问题被认为是该理论的应用。