Multi-Objective Generalized H2 Control for Optimal Protection from Vibration

Multi-objective control problems with generalized $H$2-norms as criteria are studied. By using a scalar multiobjective cost function in the form of Germeyer convolution we derive necessary conditions for Pareto optimality and characterize Pareto optimal controllers in terms of LMIs as optimal solutions for this function. Vibration isolation and attenuation problems are then considered in such a novel framework and Pareto optimal isolators and controllers are synthesized for basic models in the problems of optimal protection from vibration. Index Terms-multi-objective optimization, Pareto optimal control, Germeyer convolution, generalized $H$2-norm, vibration isolation and attenuation